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1. Weakly Differentiable Functions:
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2. Metric Spaces
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3. An Introduction to Hilbert Space
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4. Elements of Mathematics: Chapters
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5. Inside the FFT Black Box: Serial
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6. Applications of Orlicz Spaces
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7. A Hilbert Space Problem Book (Graduate
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8. Non-Linear Elastic Deformations
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9. Theory of Linear Operators in
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10. Introduction to the Analysis of
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11. Transform Circuit Analysis for
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12. Invariant Subspaces
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13. Theory of Hp Spaces
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14. Introduction To Fourier Optics
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15. An Introduction to Hilbert Space
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16. Introduction to Operator Space
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17. An Introduction to Models and
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18. Classical Banach Spaces I And
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19. Integral Transforms, Reproducing
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20. Function Spaces, Entropy Numbers

1. Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics)
by William P. Ziemer
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Asin: 0387970177
Catlog: Book (1989-08-01)
Publisher: Springer-Verlag
Sales Rank: 632264
Average Customer Review: 5 out of 5 stars
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Book Description

The major thrust of this book is the analysis of pointwise behavior of Sobolev functions of integer order and BV functions (functions whose partial derivatives are measures with finite total variation). The development of Sobolev functions includes an analysis of their continuity properties in terms of Lebesgue points, approximate continuity, and fine continuity as well as a discussion of their higher order regularity properties in terms of Lp-derivatives. This provides the foundation for further results such as a strong approximation theorem and the comparison of Lp and distributional derivatives. Also included is a treatment of Sobolev-Poincaré type inequalities which unifies virtually all inequalities of this type. Although the techniques required for the discussion of BV functions are completely different from those required for Sobolev functions, there are similarities between their developments such as a unifying treatment of Poincaré-type inequalities for BV functions. This book is intended for graduate students and researchers whose interests may include aspects of approximation theory, the calculus of variations, partial differential equations, potential theory and related areas. The only prerequisite is a standard graduate course in real analysis since almost all of the material is accessible through real variable techniques. ... Read more

Reviews (1)

5-0 out of 5 stars excellent resource
The function spaces discussed in this book are the natural ones in which to look for solutions of Partial Differential Equations and of problems in the Calculus of Variations (and so I don't think the material is esoteric!). This book is simply necessary for analysts and for anyone interested in rigor in the context of PDE. It is not as readable as the book by Evans and Gariepy, which is a pleasure to read cover to cover, but it contains more information and discusses some more technical spaces. ... Read more


2. Metric Spaces
by Victor Bryant
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Asin: 0521318971
Catlog: Book (1985-05-02)
Publisher: Cambridge University Press
Sales Rank: 310535
Average Customer Review: 4.67 out of 5 stars
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Book Description

Here is an introductory text on metric spaces that is the first to be written for students who are as interested in the applications as in the theory. Knowledge of metric spaces is fundamental to understanding numerical methods (for example for solving differential equations) as well as analysis, yet most books at this level emphasise just the abstraction and theory. Dr Bryant uses applications to provide motivation and to sustain the development and discusses numerical procedures where appropriate. The reader is expected to have had some exposure to elementary analysis, but the author provides examples throughout to refresh the student's memory and to test and extend understanding. In short, this is an introductory textbook that will appeal to students of mathematics and engineering and will give them the required background for more advanced courses in both analysis and numerical analysis. ... Read more

Reviews (3)

5-0 out of 5 stars Great Introduction to Metric Spaces. Lively, Informal Style
This short book is a gem. Metric Spaces is an especiallywell-written introduction to analysis. I liked the author's informalconversational approach to a rather abstract topic. Although I did find it necessary to reread substantial sections for full understanding, I found Metric Spaces to be quite enjoyable.

Dr. Bryant motivates the reader immediately with a look at iterative techniques, fixed point functions, converging sequences, and approximation solutions - all in an engaging style. Later topics included distance concepts, function spaces, and the relationship between closed sets, complete sets, and compact sets. The fourth chapter was devoted to the contraction mapping principle and its use in solving differential equations.

Is this book for you? The author says: "The only prerequisite is to have done a course on elementary analysis: it is not a prerequisite to have understood it nor to have remembered it at all." I personally had no formal courses in real or functional analysis and the highly structured axiomatic approach of analysis texts had never appealed to me. I only had a vague idea as to the properties of a metric space. But I was lured into buying Dr. Bryant's short text by the previous Amazon reviewers. And thankfully so.

Dr. Bryant clearly enjoys his subject, but he just as clearly recognizes that not everyone might have such an abiding interest. Throughout the text, he points out opportunities where the reader might skip forward if the going has become less interesting. (For the record I refused to be enticed by these short cuts.)

Problems are embedded in the text, one or two at a time, and are used to reinforce points under discussion. Most have clear hints and I found many problems straightforward, but others were more difficult. A few problems were identified as appropriate for the "keen" student.

The most abstract mathematics are reserved for the last (optional) chapter, but the author does encourage the reader to stay with it: "It would be a pity to stop ..." Chapter five recasts the first four chapters into a more generalized form of real analysis and addresses the question: "What makes analysis work?"

Dr. Bryant had an unusual goal for a mathematics text. "I have tried to provide a readable and natural introduction to an abstract subject in a down-to-earth manner." Also, he says, "My aim is to provide a book which can be read and enjoyed ..." He succeeded in doing just that.

5-0 out of 5 stars Metric Spaces
A short but excellent book for someone who wants a well motivated refresher on analysis. By grounding the ideas with applications of fixed point theorems (such as proving the existence of unique solutions to certain types of differential equations) the author makes accessible an area of mathematics that is often treated in an axiomatic and uninteresting way.

I believe the author is correct when he recommends the book for people who have already had some exposure to analysis. At best a student should already have completed the standard non-rigorous college calculus sequence to get the most out of this book.

4-0 out of 5 stars This is a great introduction to fixed-point methods.
This little book can take a bright high school student or undergraduate through some most interesting territory, previously uncharted at this level of mathematical understanding. Fixed point methods -- approaches to problem solving based on the simple equation f(x)=x -- are ubiquitous and ideally suited for digital computers, but they are seldom introduced in the classroom. Get this book for your high school library. Use it as an independent study for that student you don't want to set loose on calculus quite yet. ... Read more


3. An Introduction to Hilbert Space
by N. Young
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Asin: 0521337178
Catlog: Book (1988-07-21)
Publisher: Cambridge University Press
Sales Rank: 132792
Average Customer Review: 4.6 out of 5 stars
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Book Description

This textbook is an introduction to the theory of Hilbert spaces and its applications. The notion of a Hilbert space is a central idea in functional analysis and can be used in numerous branches of pure and applied mathematics. Dr. Young stresses these applications particularly for the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis.Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. The book is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). The book will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design. ... Read more

Reviews (5)

5-0 out of 5 stars GOOD for control theory theory
This book is good to any control engineer who wants to know the background theory of optimization and robust control, but read read an analysis book first.

4-0 out of 5 stars A Tantalizing Introduction to Hilbert Space
Young has done an admirable job at presenting some really beautiful and useful aspects of Hilbert spaces in a manner comprehendable for advanced undergraduates. After reading the book and reflecting on the experience, I'm somewhat amazed at the amount of nice ideas that were presented in such a compact text. The book cannot be compared with more rigorous and comprehensive texts such as Rudin, but you still get all the fundamentals of Hilbert space plus some wonderful applications.

I must strongly disagree with the reader from Sao Paolo who says that chapters 12 and 13 are poorly motivated. These chapters are crucial for the final theorem of the book in chapter 16. Parrott's Theorem in chapter 12 is the key to the foundational Nehari's theorem of chapter 15. Chapter 13 explores Hardy spaces which are the setting place for the major theorem of Adamyan, Arov, and Krein in chapter 16. In fact, I found the movement of ideas from chapter 12 to chapter 16 to be marvelously compelling. These chapters have extreme importance for theoretically oriented control engineers.

Only a modicum of real and complex analysis is necessary to understand the book. Knowledge of measure theory is not required.

5-0 out of 5 stars Very Clear,short and useful
The first eleven chapters are an excellent introduction to functional analysis . Both Hilbert and Banach spaces are introduced carefully. Then there are two short chapters on orthogonal expansions and classical fourier series and then linear operators are studied. From the point of view of a person who is interested in applications to physics and engineering one can say that the book is well motivated mainly because is so compact and because of the many notes on applications. Chapters nine , ten and eleven on Green's functions and eigenfunctions expansions are extremely good. Chapters twelve and thirteen are poorly motivated from the point of view of applications.Finally chapters fourteen to sixteen try to exhibit the applications to complex analysis of operator theory and be helpfull to eletrical engineers.I think the book fails in this. So the ten first chapters of the book are excellent . The remaining less so

5-0 out of 5 stars An unusually readable book on Hilbert space
An unusually readable book on Hilbert space. Very clean notation and very detailed proofs. There are also numerous diagrams. There are also answers to selected problems, but no detailed solutions. If you own one book on Hilbert space, or even functional analysis, this should be it. The author takes great pains to illustrate the ideas involved, not just pound out the theorems.

4-0 out of 5 stars Concise and accurate introduction to Hilbert space
I found this book a concise, well written and accurate introduction to linear algebra. Although some fellow students told me they found it too dry, I had no problem with that. ... Read more


4. Elements of Mathematics: Chapters 1-5
by N. Bourbaki, H. G. Eggleston, S. Madan
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Asin: 3540423389
Catlog: Book (2002-12-16)
Publisher: Springer Verlag
Sales Rank: 477744
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Book Description

This is a softcover reprint of the English translation of 1987 of the second edition of Bourbaki's Espaces Vectoriels Topologiques (1981). This second edition is a brand new book and completely supersedes the original version of nearly 30 years ago. But a lot of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, all reflecting the progress made in the field during the last three decades. ... Read more


5. Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms
by Eleanor Chu, Alan George
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Asin: 0849302706
Catlog: Book (1999-11-11)
Publisher: CRC Press
Sales Rank: 713568
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Book Description

Are some areas of fast Fourier transforms still unclear to you? Do the notation and vocabulary seem inconsistent? Does your knowledge of their algorithmic aspects feel incomplete? The fast Fourier transform represents one of the most important advancements in scientific and engineering computing. Until now, however, treatments have been either brief, cryptic, intimidating, or not published in the open literature. Inside the FFT Black Box brings the numerous and varied ideas together in a common notational framework, clarifying vague FFT concepts.Examples and diagrams explain algorithms completely, with consistent notation. This approach connects the algorithms explicitly to the underlying mathematics. Reviews and explanations of FFT ideas taken from engineering, mathematics, and computer science journals teach the computational techniques relevant to FFT. Two appendices familiarize readers with the design and analysis of computer algorithms, as well.This volume employs a unified and systematic approach to FFT. It closes the gap between brief textbook introductions and intimidating treatments in the FFT literature. Inside the FFT Black Box provides an up-to-date, self-contained guide for learning the FFT and the multitude of ideas and computing techniques it employs. ... Read more


6. Applications of Orlicz Spaces (Pure and Applied Mathematics (Marcel Dekker))
by M. M. Rao, Z. D. Ren
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Asin: 0824707303
Catlog: Book (2002-02-01)
Publisher: Marcel Dekker
Sales Rank: 1212045
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7. A Hilbert Space Problem Book (Graduate Texts in Mathematics)
by P.R. Halmos
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Asin: 0387906851
Catlog: Book (1982-11-08)
Publisher: Springer
Sales Rank: 324484
Average Customer Review: 5.0 out of 5 stars
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Reviews (1)

5-0 out of 5 stars Deserves 10 stars
This book should have been titled "A Hilbert Space Idea/Problem Book" as it not only challenges the reader to work out interesting problems in operator theory and the geometry of Hilbert space, but also motivates the essential ideas behind these fields. It is definitely a book that, even though out-of-print, will be referred to by many newcomers to operator theory and quantum physics. The insight one gains by the reading of this book is unequaled in any other books in existence on operator theory. It is becoming more rare as mathematics advances, to find books that attempt to explain the intuition behind the abstractions that are manifested in any area of mathematics. The problems in the book deal with both concrete examples and general theorems, and the reader should attempt to try and solve them without looking at the hints. The solutions found by the reader can then be compared with the author's, and some interesting differences will occur.

There are so many interesting discussions in this book that to list them all would probably entail listing everything in the book. The reader will find excellent discussions of the origin of normal operators on infinite dimensional Hilbert spaces as analogs to matrices on finite dimensional spaces; why the weak topology in infinite dimensions is not metrizable; the non-emptiness of the spectrum and why the spectral radius can be computed even though the spectrum cannot; the impossibility of isolated singular operators; the non-continuity of the spectrum: the existence of an operator with a large spectrum and the existence of operators with small spectra in every neighborhood of the large spectrum. The author then goes on to show that the spectrum is an upper semicontinuous function, thus preventing the existence of small spectra arbitrarily close to large spectra. This is an excellent discussion on the meaning and intuition behind semicontinuity; the result that every normal operator is unitarily equivalent to a multiplication and its equivalance to the spectral theorem. The author goes on to explain how one gives up the sigma-finiteness of the measure when doing this, and the origin of functional calculus; the difference between infinite and finite dimensions when attempting a polar decomposition for operators and its connection with partial isometries; the origin of compact operators and their connection with integral equations. The author shows how even the identity operator is not an integral operator on the space of square-integrable functions with Lebesgue measure.

In discussing the spectral theorem in chapter 13 the author statesmost profoundly: "In some contexts some authors choose to avoid a proof that uses the spectral theorem even if the alternative is longer and more involved. This sort of ritual circumlocution is common to many parts of mathematics; it is the fate of many big theorems to be more honored in evasion than in use. The reason is not just mathematical mischievousness. Often a long but 'elementary' proof gives more insight, and leads to more fruitful generalizations, than a short proof whose brevity is made possible by a powerful but overly specialized tool." In these few sentences the author has characterized the problem with current methods of teaching advanced mathematics. Too often the formalism masks the true meaning and intuitive motivation behind the mathematics. And even though mathematics is being applied to many different areas at an unprecedented rate, pure mathematics seems to be trapped in a local minimum, and I beleive this is due to the reluctance of authors to explain in detail the essentials of their ideas. This book is a perfect example of how mathematics can be taught that requires much thought and creativity on the part of students, without spoon-feeding them and thus encouraging a passive attitude to the learning of mathematics. I salute the author in his achievements in research and in teaching...one can only hope that his approach will be followed in all future works of mathematics. ... Read more


8. Non-Linear Elastic Deformations
by R. W. Ogden
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Asin: 0486696480
Catlog: Book (1997-06-01)
Publisher: Dover Publications
Sales Rank: 163308
Average Customer Review: 2 out of 5 stars
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Book Description

Meticulous, precise account of the theory of finite elasticity covers the application of the theory to the solution of boundary-value problems, and to the analysis of the mechanical properties of solid materials capable of large elastic deformations. Setting is purely isothermal. Widely regarded as a classic in the field. Problems. References. Appendixes. 544p.
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Reviews (3)

4-0 out of 5 stars A defense of Ogden
It is easy to see why other reviewers do not like this book: it is very advanced. It is not for an undergraduate, and probably not for a graduate student unless she or he is already very familiar with elasticity and solid mechanics. It is not, at bottom, a text for learning the rudiments of the theory of elasticity: it is more on the level of a research monograph, and Malvern or Fung are better choices for many students. However, Ogden is probably the best work available (other than perhaps Truesdell, who can be an acquired taste) on the rigourous theory of non-linear elasticity. If you have an interest in the structure of constitutive relations, need a rigourous mathematical reference for finite element modeling, or are interested in exploring the assumptions and limitations of the linearised theory of elasticity, Ogden is not just the best place to start, but possibly the only place to go.

1-0 out of 5 stars If you can't teach it, you don't understand it.
This is a horribly written book. Instead of teaching non-linear elasticity to the reader, Ogden hides behind jargon and notation. Perhaps if you know finite elasticity very well, it would serve as a good reference.

If you are interested in learning continuum mechanics, I recommend starting with Introduction to the Mechanics of a Continuous Medium, by L. E. Malvern. Then continue with Nonlinear Solid Mechanics: A Continuum Approach for Engineers, by G. A. Holzapfel.

1-0 out of 5 stars Not good.
I have a big problem with the Dover series to which this book belongs. The price may look good, but explanations are brief and visual representations of subjects treated are sparse. Don't buy this book. ... Read more


9. Theory of Linear Operators in Hilbert Space
by N. I. Akhiezer, I. M. Glazman
list price: $17.95
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Asin: 0486677486
Catlog: Book (1993-12-16)
Publisher: Dover Publications
Sales Rank: 67094
Average Customer Review: 4.5 out of 5 stars
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Book Description

This classic textbook by two mathematicians from the U.S.S.R.’s prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.
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Reviews (2)

5-0 out of 5 stars A Dover classic.
The spectral theorem of David Hilbert, John von Neumann, and Marshall Stone gives a complete answer to the question of which operators admit a diogonal representation, up to unitary equivalence, and makes the question precise as well. The theorem states that these are the normal operators in Hilbert space. This includes the selfadjoint operators which represent observables in quantum physics, and the more interesting ones are unbounded. Remember the Heisenberg commutation relations do not admit bounded solutions. But there is a mathematical distinction between formally selfadjoint operators (also called symmetric operators) and the selfadjoint ones. It is only the latter to which the spectral theorem applies. The distinction between the two is understood from a pair of indicies (n,m), now called deficiency indices. In some applications they represent
boundary conditions, and when n = m, and the boundary conditions are assigned, the symmetric operator in question has selfadjoint extensions. And we know from von Neumann what they are. A central question in the book concerns the issue of unequal indices. Then selfadjoint extensions do not exist, at least not unless the Hilbert space is enlarged. A central theme in the book is that in case of unequal indices, there is a larger Hilbert space which does in fact admit selfadjoint extensions. The co-authors, along with Naimark, are the authorities on this. Because of applications to PDE theory and to physics, there has been constant interest in the theme right up to the present. Even the current interest, and lively activity, in quantum measurement theory (in connection with quantum information theory) and entanglement brings back to to the fore this old issue around diagonalizing operators by passing to an "enlarged" (or dilated)Hilbert space, or looking for an orthonormal basis in the extended Hilbert space. So the theme of the book is still current.

4-0 out of 5 stars Such an easy book to read!
This is a great intro to functional analysis. Having taken a graduate course on the subject, I used this as my text. The proofs are very readable and kept clear and simple. You'll see the subject develop before your eyes. One thing: when reading this book on infinite dimensional vector spaces, always try to draw a parallel with the finite dimensional version of the subject, linear algebra. You'll appreciate the book all the more. For every theorem relating to a bounded linear operator on Hilbert space, replace the operator by a matrix on Euclidean n-space.. you'll say "oh yeah! I remember that from linear algebra!" ... Read more


10. Introduction to the Analysis of Metric Spaces (Australian Mathematical Society Lecture Series)
by John R. Giles
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Asin: 0521359287
Catlog: Book (1987-09-03)
Publisher: Cambridge University Press
Sales Rank: 1360947
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Book Description

Assuming a basic knowledge of real analysis and linear algebra, the student is given some familiarity with the axiomatic method in analysis and is shown the power of this method in exploiting the fundamental analysis structures underlying a variety of applications.Although the text is titled metric spaces, normed linear spaces are introduced immediately because this added structure is present in many examples and its recognition brings an interesting link with linear algebra; finite dimensional spaces are discussed earlier.It is intended that metric spaces be studied in some detail before general topology is begun. This follows the teaching principle of proceeding from the concrete to the more abstract.Graded exercises are provided at the end of each section and in each set the earlier exercises are designed to assist in the detection of the abstract structural properties in concrete examples while the latter are more conceptually sophisticated. ... Read more


11. Transform Circuit Analysis for Engineering and Technology (4th Edition)
by William D. Stanley
list price: $130.00
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Asin: 0130200352
Catlog: Book (1999-06-24)
Publisher: Prentice Hall
Sales Rank: 588745
Average Customer Review: 5 out of 5 stars
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Reviews (1)

5-0 out of 5 stars Excellent Electrical Engineering Reference Book
I recently tutored a co-worker for the electrical engineering Professional Engineering license exam and this book greatly helped out in explaining Laplace transforms. The book covers transform circuit analysis by starting out with the basics and then building up to Laplace transforms. After reading this book and working through the examples, I feel much stronger in this area of electrical engineering. I have a B.S. in electrical engineering and a P.E. license since 1995. I have read several other books on this subject, including differential equations text books and I think this book presents the clearest explanations and examples applied directly to electrical engineering. I would recommend this book to anyone with an interest in electrical engineering. ... Read more


12. Invariant Subspaces
by Heydar Radjavi, Peter Rosenthal
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Asin: 0486428222
Catlog: Book (2003-07-15)
Publisher: Dover Publications
Sales Rank: 709356
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Book Description

This broad survey spans a wealth of studies on invariant subspaces, focusing on operators on separable Hilbert space. Largely self-contained, it requires only a working knowledge of measure theory, complex analysis, and elementary functional analysis. Subjects include normal operators, analytic functions of operators, shift operators, examples of invariant subspace lattices, compact operators, and the existence of invariant and hyperinvariant subspaces. Additional chapters cover certain results on von Neumann algebras, transitive operator algebras, algebras associated with invariant subspaces, and a selection of unsolved problems. 1973 ed. New appendix on recent developments.
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13. Theory of Hp Spaces
by Peter L. Duren
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Asin: 0486411842
Catlog: Book (2000-08-01)
Publisher: Dover Publications
Sales Rank: 537699
Average Customer Review: 5 out of 5 stars
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Book Description

A blend of classical and modern techniques and viewpoints, this text examines harmonic and subharmonic functions, the basic structure of Hp functions, applications, conjugate functions, and mean growth and smoothness. Other subjects include Taylor coefficients, Hp as a linear space, interpolation theory, the corona theorem, and more. Information on Rademacher functions and maximal theorems appears in the appendixes. Essentially self-contained, with a list of exercises in each chapter, this text is appropriate for researchers or second- or third-year graduate students.1970 ed.
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Reviews (1)

5-0 out of 5 stars This book is a classic
The first edition of this book appeared about thirty years ago and unfortunately wasn't very popular as a textbook because of its limited availability. This new edition makes it possible for many readers (including me) to own it at last. The book is written from the viewpoint of classical analysis and is as fresh now as it was 30 years ago despite huge progress made in this area during the last decades. Both organization and selection of material is excellent and introduces the reader to one of the most beautiful mathematical theories created in 20th century. The author took his time and wrote a very informative Supplement. It not just covers the newest developments in the theory of Hardy spaces and problems solved in last thirty years, but also gives very good idea about newest directions which grew up from this theory. This book definitely should be recommended to any student who wants to specialize in the theory Banach spaces of analytic or harmonic functions. ... Read more


14. Introduction To Fourier Optics
by Joseph W Goodman
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Asin: 0070242542
Catlog: Book (1996-01-01)
Publisher: McGraw-Hill Science/Engineering/Math
Sales Rank: 59574
Average Customer Review: 4.75 out of 5 stars
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Book Description

The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the field. All the material has been update and several new sections explore the recent progress made in the areas of wavelength modulation, analog information processing, and holography. The book also explores Fourier analysis applications and emphasizes those applications to diffraction, imaging, optical data processing, and holography. ... Read more

Reviews (4)

4-0 out of 5 stars A good path to physical optics and imaging theory
This book is cleary written. The basic theory of Fourier transform is included too. Fourier optics is a very strong tool in imaging and optics. I would say Goodman is an enginnering guy, but some physical insight is not very clear. Diffraction theory is easier to understand than J.D. Jackson's E&M. And the whole book is easier to read than Born and Wolf's Principle of Optics and has more details. After all, it is a good book for Fourier opitcs. But the price is too high.

5-0 out of 5 stars optics
I am study to work with optical design programs Zemax. I wonna know theory to use in this programme. my e-mail: all_ladis@ipm.lviv.ua

5-0 out of 5 stars Clearly the Best Fourier Optics Book
Joseph Goodman has done a stellar job of clearly presenting concepts AND mathematical background. There is an excellent mix of straightforward theory and practical uses of Fourier Optics. The chapter problems are very challenging but insightful. This is the best optics book I have ever read.

5-0 out of 5 stars A classic made better.
Joe Goodman is rightly famous for his clear writing, teaching and thinking. I especially appreciate the clear boundaries that he draws around the segments of his subject: it is clear what is known & unknown, what is easy & what is hard. This book is worth having and studying as an example of how to write a textbook, not only for its subject matter. ... Read more


15. An Introduction to Hilbert Space and Quantum Logic (Problem Books in Mathematics)
by David W. Cohen
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Asin: 0387968709
Catlog: Book (1989-06-01)
Publisher: Springer-Verlag
Sales Rank: 770408
Average Customer Review: 4 out of 5 stars
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Book Description

Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence each other we hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed. ... Read more

Reviews (1)

4-0 out of 5 stars Effective introduction
This book gives a nice introduction to the mathematical formalism behind quantum physics and the logic of measurement. The first chapter gives an introduction to measure theory with emphasis on probabilities of measurement outcomes. The author is careful to point out that the calculation of the Lebesgue integral presents more difficulties than in the Riemann integral case, since the fundamental theorem of calculus does not apply to Lebesgue integrals.

This is followed by an elementary introduction to Hilbert space in Chapter 2. This is standard material and most of the proofs of the main results are omitted and left to the reader as projects.

Chapter 3 is more controversial, and attempts to formulate a logic of experimentation for "non-classical" systems. This is done by use of what the author calls a "manual", which is viewed as an abstraction of the experimenters knowledge about a physical system. A manual is a collection of experiments, and an "event" is a subset of an experiment. Orthogonality of events is defined, along with the notion of a collection of events being "compatible", meaning that there is an experiment that contains all of these events. A manual is called "classical" if every pair of events is compatible. The author then exhibits systems that are not classical via the double-slit and Stern-Gerlach experiments. A logic of events is then developed in the next section, where quantum logic is defined explicitly. The author defines a pure state that is not dispersion-free as a state of ontological uncertainty as opposed to "epistemic" uncertainty. Quantum systems have states that are ontologically uncertain according to the author. The author chooses not to engage in the debate about the actual existence of these states and, accordingly, no real-world experiments are given to illustrate the relevance of the concepts and definitions.

The next chapter covers the geometry of infinite-dimensional Hilbert spaces. The structure of the collection of these subspaces is defined in terms of the quantum logic defined earlier. This is followed by a discussion of maps on Hilbert spaces, as preparation for defining observables in quantum systems. The important Riesz representation theorem is stated but the proof left to the reader. Projection operators are defined also with the eventual goal of relating them to the compatibility of two propositions.

Gleason's theorem is discussed in Chapter 6, along with a discussion of the geometry of state space. The proof of Gleason's theorem is omitted, the author emphasizing its difficulty. The proof in the literature is non-constructive and thus the theorem is suspect according to some schools of thought.

The spectral theorem, so important in quantum physics, is discussed in the next chapter. Once again the proofs are left to the reader for most of the results. The spectral theorem allows the author to define another notion of compatibility in terms of the commutativity of two Hermitian operators.

The books ends with a overview of the EPR dilemna and is naturally more controversial than the rest of the book. This topic has provoked much philosophical debate, and the author gives the reader a small taste of this in this chapter.

The book does serve its purpose well, and regardless of one's philosophical position on quantum physics, the mathematical formulations of quantum physics and measurement theory are nicely expounded in this book. ... Read more


16. Introduction to Operator Space Theory (London Mathematical Society Lecture Note Series)
by Gilles Pisier
list price: $55.00
our price: $51.15
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Asin: 0521811651
Catlog: Book (2003-08-25)
Publisher: Cambridge University Press
Sales Rank: 972865
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Book Description

The first part of this book is an introduction with emphasis on examples that illustrate the theory of operator spaces. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C* algebras. The third part of the book describes applications to non self-adjoint operator algebras and similarity problems. The author's counterexample to the "Halmos problem" is presented, along with work on the new concept of "length" of an operator algebra. ... Read more


17. An Introduction to Models and Decompositions in Operator Theory
by Carlos S. Kubrusly
list price: $64.95
our price: $64.95
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Asin: 0817639926
Catlog: Book (1997-03-01)
Publisher: Birkhauser Boston
Sales Rank: 1429460
Average Customer Review: 5 out of 5 stars
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Reviews (1)

5-0 out of 5 stars Nice and well organized introduction to a difficult subject
The book is a very nice introduction to the subject of Models and Decompositions of operators. In reality, it is a post-introductory book. Anyone that has already studied operator Theory in Hilbert spaces and wants a deeper understanding of this subject, should have a look here, mainly because the book coherently organizes this subject that would otherwise require a large bibliographical research. Models and Decompositons are looked as a sub-product of the search for the "Holy Graal" of operator theory: The Invariant Subspace Problem. Although it is not a book about that subject, it is certainly a relevant book to anyone entering that field, because it mentions relatively recent results that were previously conjectures in that area. Particularly interesting, in my opinion, are chapters 7 and 8. Chapter 7, called "Applications", in which the theory developed in the previous chapters is applied and many interesting related problems, some of them still open, relative to strong and weak stability of operators are mentioned. Chapter 8 discusses the problem of similarity to contractions, and leaves the reader with two related open questions. ... Read more


18. Classical Banach Spaces I And Ii: Sequence Spaces; Function Spaces (Classics in Mathematics)
by Joram Lindenstrauss, Lior Tzafriri
list price: $49.95
our price: $36.46
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Asin: 3540606289
Catlog: Book (2001-12-30)
Publisher: Springer-Verlag
Sales Rank: 443997
Average Customer Review: 5 out of 5 stars
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Book Description

From the reviews: "... the book is written in the best tradition of the beautiful series in which it appears. The material it presents is hard to find in other books. For people working in the structure theory of Banach spaces it will be most valuable as a source of references and inspiration. For those who wish to learn the subject the book deserves a warm welcome too." Mededelingen van het Wiskundig Genootschap "... The geometry of Banach lattices is a rich, beautiful, ... and rewarding subject. The proof is in the reading and perusing of the masterpiece." Zentralblatt für Mathematik ... Read more

Reviews (1)

5-0 out of 5 stars Great Book
This book is an excellent survey of Banach Space Theory, and an invaluable resource. It's too terse, but then again, most reference books are. ... Read more


19. Integral Transforms, Reproducing Kernels and Their Applications
by S. Saitoh
list price: $99.95
our price: $99.95
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Asin: 0582317584
Catlog: Book (1997-05-28)
Publisher: Chapman & Hall/CRC
Sales Rank: 1348917
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Book Description

The general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind. ... Read more


20. Function Spaces, Entropy Numbers and Differential Operators (Cambridge Tracts in Mathematics)
by D. E. Edmunds, H. Triebel
list price: $80.00
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Asin: 0521560365
Catlog: Book (1996-08-28)
Publisher: Cambridge University Press
Sales Rank: 2057717
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Book Description

The distribution of the eigenvalues of differential operators has long fascinated mathematicians. Recent advances have shed new light on classical problems in this area, and this book presents a fresh approach, largely based on the results of the authors. The emphasis here is on a topic of central importance in analysis, namely the relationship between i) function spaces on Euclidean n-space and on domains; ii) entropy numbers in quasi-Banach spaces; and iii) the distribution of the eigenvalues of degenerate elliptic (pseudo) differential operators. The treatment is largely self-contained and accessible to nonspecialists. ... Read more


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