Book Description

The aim of this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory leading to an elementary proof of the Lidskij trace theorem. The author assumes the reader is familiar with linear algebra and advanced calculus, and develops everything needed to introduce the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators. Many exercises and hints are included, and throughout the emphasis is on a user-friendly approach. ... Read more

Book Description

In this tract, Dr Ruston presents analogues for operators on Banach spaces of Fredholm's solution of integral equations of the second kind. Much of the presentation is based on research carried out over the last twenty-five years and has never appeared in book form before. Dr Ruston begins with the construction for operators of finite rank, using Fredholm's original method as a guide. He then considers formulae that have structure similar to those obtained by Fredholm, using, and developing further, the relationship with Riesz theory. In particular, he obtains bases for the finite-dimensional subspaces figuring in the Riesz theory. Finally he returns to the study of specific constructions for various classes of operators. Dr Ruston has made every effort to keep the presentation as elementary as possible, using arguments that do not require a very advanced background. Thus the book can be read with profit by graduate students as well as specialists working in the general area of functional analysis and its applications. ... Read more

Book Description

Replete with easy-to-understand examples ranging from the prediction of home runs in baseball using an hierarchical Bayesian statistics model to estimating the expected return at blackjack using control variables, this text functions as a complete consideration of simulation. Sheldon Ross provides broad yet thorough coverage of the subject, presenting the development of a simulation study to analyze models, and demonstrates that by using random variables and the concept of discrete events, it is possible to generate the behavior of a stochastic model over time. Also discussed are questions concerning when to stop a simulation, how much confidence can be placed in the results, and extensive new information on the presentation of the alias method for generating discrete random variables material not found in any other text. Students, practitioners, and researchers alike will find this text to have an important place in their research libraries.

* Presents the statistics needed to analyze simulated data as well as those needed for validating the simulation model
* Stresses variance reduction, including control variables and their relation to regression analysis
* Includes a chapter on Markov chain monte carlo methods
* Emphasizes the use of computers throughout the text ... Read more

Reviews (1)

A reader from Saudi Arabia
This is an excelent textbook explaining what simulation means and how to deepen your knowalge. You have to be a good programmer in order to use this book (and simulation generally)and the author should have added an andex for such a language and how its connection with simualtion ( C or C++) although my experience would elect MATLAB as prefernce!! This text does not requir any prior experience regarding simulatin although taking a course in statistics and probability would be advantageous!! ... Read more

Book Description

Providing valuable new tools for specialists in functional analysis and stability theory, this state-of-the-art reference presents a systematic exposition of estimations for norms of operator-valued functions and applies the estimates to spectrum perturbations of linear operators and stability theory.Demonstrating a novel approach to spectrum perturbations, Norm Estimations for Operator-Valued Functions and Applicationsconsiders a common procedure for the stability analysis of various classes of equationsextends the well-known spectrum perturbation result for self-adjoint operators to quasi-Hermitian operatorsexamines spectrum perturbations of operators on a tensor product of Hilbert spacescovers systems of ordinary differential equationsdeal with retarded systemsstudies the absolute stability of systems of Volterra equationsemphasizes semilinear evolution equations and more! ... Read more

Book Description

Ideal spaces are a very general class of normed spaces of measurable functions, which includes e.g. Lebesgue and Orlicz spaces. Their most important application is in functional analysis in the theory of (usual and partial) integral and integro-differential equations. The book is a rather complete and self-contained introduction into the general theory of ideal spaces. Some emphasis is put on spaces of vector-valued functions and on the constructive viewpoint of the theory (without the axiom of choice). The reader should have basic knowledge in functional analysis and measure theory. ... Read more

Book Description

This volume gives an account of the current state of weight theory for integral operators, such as maximal functions, Riesz potential, singular integrals and their generalization in Lorentz and Orlicz spaces. Starting with the crucial concept of a space of homogeneous type, it continues with general criteria for the boundedness of the integral operators considered, then address special settings and applications to classical operators in Euclidean spaces. ... Read more

Book Description

This volume reflects the progress made in many branches of recent research in Banach space theory, an analytic approach to geometry. Including papers by most of the leading figures in the area, it is intended to illustrate the interplay of Banach space theory with harmonic analysis, probability, complex function theory, and finite dimensional convexity theory. The papers consist of a selection of surveys and original research. ... Read more

Book Description

One of the most exciting features of the fields of Radontransforms and tomography is the strong relationship betweenhigh-level pure mathematics and applications to areas such asmedical imaging and industrial nondestructive evaluation. Theproceedings featured in this volume bring together fundamentalresearch articles in the major areas of Radon transforms andtomography.

This volume includes expository papers that are of specialinterest to beginners as well as advanced researchers. Topicsinclude local tomography and wavelets, Lambda tomography andrelated methods, tomographic methods in RADAR, ultrasound, Radontransforms and differential equations, and the Pompeiu problem.

The major themes in Radon transforms and tomography arerepresented among the research articles. Pure mathematicalthemes include vector tomography, microlocal analysis, twistortheory, Lie theory, wavelets, harmonic analysis, anddistribution theory. The applied articles employ high-qualitypure mathematics to solve important practical problems.Effective scanning geometries are developed and tested for aNASA wind tunnel. Algorithms for limited electromagnetictomographic data and for impedance imaging are developed andtested. Range theorems are proposed to diagnose problems withtomography scanners. Principles are given for the design ofX-ray tomography reconstruction algorithms, and numericalexamples are provided.

This volume offers readers a comprehensive source of fundamentalresearch useful to both beginners and advanced researchers inthe fields. ... Read more

Book Description

The notion of symmetry is important in many disciplines, including physics, art, and music. The modern mathematical way of treating symmetry is through transformation groups. This book offers an easy introduction to these ideas for the relative novice, such as undergraduates in mathematics or even advanced undergraduates in physics and chemistry.

The first two chapters provide a warm-up to the material with, for example, a discussion of algebraic operations on the points in the plane and rigid motions in the Euclidean plane. The notions of a transformation group and of an abstract group are then introduced. Group actions, orbits, and invariants are covered in the next chapter. The final chapter gives an elementary exposition of the basic ideas of Sophus Lie about symmetries of differential equations.

Throughout the text, examples are drawn from many different areas of mathematics. Plenty of figures are included, and many exercises with hints and solutions will help readers master the material. ... Read more

Book Description

This up-to-date account brings together results previously scattered throughout the literature as well as new material in the area of function theory. The focus is on describing some of what has been learned thus far about the structure of the de Branges-Rovnyak spaces and their function-theoretic connections. ... Read more