Book Description

Now in paperback, this popular book gives a self-contained presentation of a number of recent results, which relate the volume of convex bodies in n-dimensional Euclidean space and the geometry of the corresponding finite-dimensional normed spaces. The methods employ classical ideas from the theory of convex sets, probability theory, approximation theory, and the local theory of Banach spaces. The first part of the book presents self-contained proofs of the quotient of the subspace theorem, the inverse Santalo inequality and the inverse Brunn-Minkowski inequality.In the second part Pisier gives a detailed exposition of the recently introduced classes of Banach spaces of weak cotype 2 or weak type 2, and the intersection of the classes (weak Hilbert space). This text will be a superb choice for courses in analysis and probability theory. ... Read more

Book Description

This book encourages readers to develop an intuitive understanding of the foundations of Linear Algebra. An emphasis on the concepts of Linear Algebra and Matrix Theory conveys the structure and nature of Linear Spaces and of Linear Transformations. Almost every chapter has three sections: a lecture followed by problems, theoretical and mathematical enrichment, and applications to and from Linear Algebra.Specific chapter topics cover linear transformations; row reduction; linear equations; subspaces; linear dependence, bases, and dimension; composition of maps, matrix inverse and transpose; coordinate vectors, basis change; determinants, …l-matrices; matrix eigenvalues; orthogonal bases and orthogonal matrices; symmetric and normal matrix eigenvalues; singular values; and basic numerical linear algebra techniques.For individuals in fields related to economics, engineering, science, or mathematics. ... Read more

Book Description

Hardbound. The Handbook presents an overview of most aspects of modern Banach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience.In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations.

The Handbook begins with a chapter on basic concepts in Banach space theory which contains all the background needed for reading any other chapter in the Handbook.Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications.Each article contains a motivated introduction as well as an exposition of the ma ... Read more

Book Description

This book is concerned with the study of algebras of linear transformation acting on finite-dimensional vector spaces, which in one guise or another arise in various parts of modern mathematics. The book's aims are: (i) to give an exposition of the basic theory of finite-dimensional algebras at a level that is appropriate for senior undergraduate and first-year graduate students, and (ii) to provide the mathematical foundation that prepares the reader for the advanced study of any one of several fields of mathematics. Indeed, the most important features of the book are the novelty of the selection of topics and the level of accessibility in which these topics are treated. The book features a relatively new approach to finite-dimensional operator algebras which is based on algebraic rather than functional-analytic methods. The reader who acquires a good understanding of the basic theory of algebras is well-positioned to appreciate results in operator algebras, representation theory, linear algebra, and ring theory. ... Read more

Book Description

This volume provides a self-contained introduction to the theory of tensor products of Banach spaces. It is written for graduate students in analysis or for researchers in other fields who wish to become acquainted with this area. The only prerequisites are a basic knowledge of functional analysis and measure theory.

Each chapter is accompanied by worked examples and a set of exercises, and two appendices provide essential material on summability in Banach spaces and properties of spaces of measures that may be new to the beginner. ... Read more

Reviews (1)

FITHIS reads
Dr Ryan gave a draft of the first chapter to my supervisor Dr Sarantopoulos . He also gave me Ryan's thesis . I was fascinated because I knew only the algebraic side of the subject . The first chapter introduced me to a some aspects of functional analysis like Rademacher techniques and nuclear operators . When the book was released I hesitated to give the money . However I thought that the rest chapters would be as great . AND this TRUE . I recommend this book to everyone wanting to learn on topological tensor products ( OK , OK , Banach space tensor products) since this understanding is essential for Banach algebras and factorization in Banach spaces . I believe in retrospect that the money are not that much for the content provided . I hope Dr Ryan will publish his thesis also . To point out how good is this book I urge you to read Barry Johnsons Cohomology of Banach algebras , both give a very good picture . Also Beuazamy's book (Operator Theory) has a proof on the dulality between N(H) and B(H) . Ryans book is essential for the explanation of this phenomenon . ... Read more

Book Description

Written in textbook style this up-to-date volume is geared towards graduate and postgraduate students and researchers interested in boundary value problems of linear differential equations or in orthogonal polynomials.

This monograph consists of three parts: - the abstract theory of Hilbert spaces, leading up to the spectral theory of unbounded self-adjoined operators; - the application to linear Hamiltonian systems, giving the details of the spectral resolution; - further applications such as to orthogonal polynomials and Sobolev differential operators. Written in textbook style this up-to-date volume is geared towards graduate and postgraduate students and researchers interested in boundary value problems of linear differential equations or in orthogonal polynomials ... Read more

Book Description

The presented collection of papers is based on lectures given at the International Conference "Function Spaces, Differential Operators and Nonlinear Analysis" (FSDONA-01) held in Teistungen, Thuringia/Germany, from June 28 to July 4, 2001.

They deal with the symbiotic relationship between the theory of function spaces, harmonic analysis, linear and nonlinear partial differential equations, spectral theory and inverse problems. This book is a tribute to Hans Triebel's work on the occasion of his 65th birthday. It reflects his lasting influence in the development of the modern theory of function spaces in the last 30 years and its application to various branches in both pure and applied mathematics. Part I contains two lectures by O.V. Besov and D.E. Edmunds having a survey character and honouring Hans Triebel's contributions. The papers in Part II concern recent developments in the field presented by D. G. de Figueiredo/C. O. Alves, G. Bourdaud, V. Maz'ya/V. Kozlov, A. Miyachi, S. Pohozaev, M. Solomyak and G. Uhlmann. Shorter communications related to the topics of the conference and Hans Triebel's research are collected in Part III ... Read more

Book Description

This book provides an overview of some of the most active topics in the theory of transformation groups over the past decades and stresses advances obtained in the last dozen years. The emphasis is on actions of Lie groups on manifolds and CW complexes. Manifolds and actions of Lie groups on them are studied in the linear, semialgebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role.The work is divided into fifteen articles and will be of interest to anyone researching or studying transformations groups. The references make it easy to find details and original accounts of the topics surveyed, including tools and theories used in these accounts. ... Read more

Book Description

"When do the Lebesgue-Bochner function spaces contain a copy or a complemented copy of any of the classical sequence spaces?" This problem and the analogous one for vectorvalued continuous function spaces have attracted quite a lot of research activity in the last twenty-five years. The aim of this monograph is to give a detailed exposition of the answers to these questions, providing a unified and self-contained treatment. It presents a great number of results, methods and techniques, which are useful for any researcher in Banach spaces and, in general, in Functional Analysis. This book is written at a graduate student level, assuming the basics in Banach space theory. ... Read more

Book Description

A problem of broad interest - the estimation of the spectral gap for matrices or differential operators (Markov chains or diffusions) - is covered in this book. In particular, it studies a subset of the general problem, taking some approaches that have, up till now, only appeared largely in the Chinese literature.Eigenvalues, Inequalities and Ergodic Theory serves as an introduction to this developing field, and provides an overview of the methods used in an accessible and concise manner.Each chapter starts with a summary and, in order to appeal to non-specialists, ideas are introduced through simple examples rather than technical proofs. In the latter chapters readers are introduced to problems and application areas, including stochastic models of economy.Intended for researchers, graduates and postgraduates in probability theory, Markov processes, mathematical physics and spectrum theory, this book will be a welcome introduction to a growing area of research. ... Read more

Book Description

This book presents the first comprehensive treatment of the blocking technique which consists in transforming norms in section form into norms in block form, and vice versa. Such norms appear throughout analysis. The blocking technique is a powerful, yet elementary, tool whose usefulnes is demonstrated in the book. In particular, it is shown to lead to the solution of three recent problems of Bennett concerning the inequalities of Hardy and Copson. The book is addressed to researchers and graduate students. An interesting feature is that it contains a dictionary of transformations between section and block norms and will thus be useful to researchers as a reference text. The book requires no knowledge beyond an introductory course in functional analysis. ... Read more

Book Description

This short course on classical Banach space theory is a natural follow-up to a first course on functional analysis. The topics covered have proven useful in many contemporary research arenas such as harmonic analysis, the theory of frames and wavelets, signal processing, economics, and physics.The book is intended for use in an advanced topics course or seminar, or for independent study.It offers a more user-friendly introduction than can be found in the existing literature and includes references to expository articles and suggestions for further reading. ... Read more

Book Description

This book is written for beginning graduate students in applied mathematics, science, and engineering, and is appropriate as a one-year course in applied mathematical techniques (although I have never been able to cover all of this material in one year). We assume that the students have studied at an introductory undergraduate level material on linear algebra, ordinary and partial differential equations, and complex variables. The emphasis of the book is a working, systematic understanding of classical techniques in a modern context. Along the way, students are exposed to models from a variety of disciplines. It is hoped that this course will prepare students for further study of modern techniques and in-depth modeling in their own specific discipline. ... Read more

Reviews (2)

Excellently organized book.
This book presents various mathematical principles in an organization I have not seen before. It starts with the idea of a transformation, then goes on to relate eigenvalues and eigenvectors to general spectral theory, explain how the need for closed function spaces naturally leads to Lebesgue integration (I know about Lebesgue integration before but I didn't know why it was needed), and show how the definition of certain inverse operators leads to distribution theory. This is a very natural way of organizing these principles. While other books, such as Strang's Intro to Applied Mathematics and Rudin's Real & Complex Analysis, provide you with one mathematical "toy" after another (Fourier series, Lebesgue integration, etc.), Keener's book tells you why you need the toy before giving it to you.

Am I stupid or this book is too advance???
This book doesn't clearify anything for you. No examples, No further explanation. It only keeps introduce various theories to you. It can compact theories that other books take 2-3 pages to explain it into 5 lines! I think you can imagine. Obviously, this book is not suitable to be your first book (not the second also). Buy it if you are sure that you are smart enough to understand it! ... Read more