An Introduction to Hilbert Space

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Author: N. Young

Publisher: Cambridge University Press

ISBN: 9780521337175

Category: Mathematics

Page: 239

View: 1178

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.

An Introduction to the Theory of Reproducing Kernel Hilbert Spaces

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Author: Vern I. Paulsen,Mrinal Raghupathi

Publisher: Cambridge University Press

ISBN: 1107104092

Category: Mathematics

Page: 192

View: 552

A unique introduction to reproducing kernel Hilbert spaces, covering the fundamental underlying theory as well as a range of applications.

Introduction to Operator Space Theory

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Author: Gilles Pisier

Publisher: Cambridge University Press

ISBN: 9780521811651

Category: Mathematics

Page: 478

View: 4933

An introduction to the theory of operator spaces, emphasising applications to C*-algebras.

Robust Control Theory in Hilbert Space

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Author: Avraham Feintuch

Publisher: Springer Science & Business Media

ISBN: 1461205913

Category: Mathematics

Page: 228

View: 8051

An operator theoretic approach to robust control analysis for linear time-varying systems, with the emphasis on the conceptual similarity with the H control theory for time-invariant systems. It clarifies the major difficulties confronted in the time varying case and all the necessary operator theory is developed from first principles, making the book as self-contained as possible. After presenting the necessary results from the theories of Toeplitz operators and nest algebras, linear systems are defined as input-output operators and the relationship between stabilisation and the existence of co-prime factorisations is described. Uniform optimal control problems are formulated as model-matching problems and are reduced to four block problems, while robustness is considered both from the point of view of fractional representations and the "time varying gap" metric, as is the relationship between these types of uncertainties. The book closes with the solution of the orthogonal embedding problem for time-varying contractive systems. As such, this book is useful to both mathematicians and to control engineers.

Wavelets

A Student Guide

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Author: Peter Nickolas

Publisher: Cambridge University Press

ISBN: 1316727939

Category: Mathematics

Page: N.A

View: 497

This text offers an excellent introduction to the mathematical theory of wavelets for senior undergraduate students. Despite the fact that this theory is intrinsically advanced, the author's elementary approach makes it accessible at the undergraduate level. Beginning with thorough accounts of inner product spaces and Hilbert spaces, the book then shifts its focus to wavelets specifically, starting with the Haar wavelet, broadening to wavelets in general, and culminating in the construction of the Daubechies wavelets. All of this is done using only elementary methods, bypassing the use of the Fourier integral transform. Arguments using the Fourier transform are introduced in the final chapter, and this less elementary approach is used to outline a second and quite different construction of the Daubechies wavelets. The main text of the book is supplemented by more than 200 exercises ranging in difficulty and complexity.

Functional Analysis

An Elementary Introduction

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Author: Markus Haase

Publisher: American Mathematical Society

ISBN: 0821891715

Category: Mathematics

Page: 372

View: 7088

This book introduces functional analysis at an elementary level without assuming any background in real analysis, for example on metric spaces or Lebesgue integration. It focuses on concepts and methods relevant in applied contexts such as variational methods on Hilbert spaces, Neumann series, eigenvalue expansions for compact self-adjoint operators, weak differentiation and Sobolev spaces on intervals, and model applications to differential and integral equations. Beyond that, the final chapters on the uniform boundedness theorem, the open mapping theorem and the Hahn-Banach theorem provide a stepping-stone to more advanced texts. The exposition is clear and rigorous, featuring full and detailed proofs. Many examples illustrate the new notions and results. Each chapter concludes with a large collection of exercises, some of which are referred to in the margin of the text, tailor-made in order to guide the student digesting the new material. Optional sections and chapters supplement the mandatory parts and allow for modular teaching spanning from basic to honors track level.

Hilbert Spaces with Applications

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Author: Lokenath Debnath,Piotr Mikusiński

Publisher: Academic Press

ISBN: 0122084381

Category: Mathematics

Page: 580

View: 1213

Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory. Updated chapter on wavelets Improved presentation on results and proof Revised examples and updated applications Completely updated list of references

A Course in Modern Mathematical Physics

Groups, Hilbert Space and Differential Geometry

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Author: Peter Szekeres

Publisher: Cambridge University Press

ISBN: 9780521829601

Category: Mathematics

Page: 600

View: 2578

This book provides an introduction to the mathematics of modern physics, presenting concepts and techniques in mathematical physics at a level suitable for advanced undergraduates and beginning graduate students. It aims to introduce the reader to modern mathematical thinking within a physics setting. Topics covered include tensor algebra, differential geometry, topology, Lie groups and Lie algebras, distribution theory, fundamental analysis and Hilbert spaces. The book includes exercises and worked examples, to test the students' understanding of the various concepts, as well as extending the themes covered in the main text.

Linear Analysis

An Introductory Course

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Author: Béla Bollobás

Publisher: Cambridge University Press

ISBN: 9780521655774

Category: Mathematics

Page: 240

View: 8156

Revised and updated introduction to functional analysis.

Introduction to the Analysis of Normed Linear Spaces

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Author: J. R. Giles,John Robilliard Giles

Publisher: Cambridge University Press

ISBN: 9780521653756

Category: Mathematics

Page: 280

View: 1620

This text is ideal for a basic course in functional analysis for senior undergraduate and beginning postgraduate students. John Giles provides insight into basic abstract analysis, which is now the contextual language of much modern mathematics. Although it is assumed that the student has familiarity with elementary real and complex analysis, linear algebra, and the analysis of metric spaces, the book does not assume a knowledge of integration theory or general topology. Its central theme concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. Giles illustrates the general theory with a great variety of example spaces.

A Mathematical Introduction to Wavelets

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Author: P. Wojtaszczyk

Publisher: Cambridge University Press

ISBN: 9780521578943

Category: Mathematics

Page: 261

View: 9378

This book presents a mathematical introduction to the theory of orthogonal wavelets and their uses in analyzing functions and function spaces, both in one and in several variables. Starting with a detailed and self-contained discussion of the general construction of one dimensional wavelets from multiresolution analysis, the book presents in detail the most important wavelets: spline wavelets, Meyer's wavelets and wavelets with compact support. It then moves to the corresponding multivariable theory and gives genuine multivariable examples. The author discusses wavelet decompositions in Lp spaces, Hardy spaces and Besov spaces and provides wavelet characterizations of those spaces. Also included are periodic wavelets or wavelets not associated with a multiresolution analysis. This will be an invaluable book for those wishing to learn about the mathematical foundations of wavelets.

Functional Analysis for Probability and Stochastic Processes

An Introduction

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Author: Adam Bobrowski

Publisher: Cambridge University Press

ISBN: 9781139443883

Category: Mathematics

Page: N.A

View: 3744

This text is designed both for students of probability and stochastic processes, and for students of functional analysis. For the reader not familiar with functional analysis a detailed introduction to necessary notions and facts is provided. However, this is not a straight textbook in functional analysis; rather, it presents some chosen parts of functional analysis that can help understand ideas from probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.

An Introduction to Hankel Operators

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Author: Jonathan R. Partington

Publisher: Cambridge University Press

ISBN: 0521366119

Category: Mathematics

Page: 103

View: 7221

Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.

Hilbert Space Methods in Signal Processing

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Author: Rodney A. Kennedy,Parastoo Sadeghi

Publisher: Cambridge University Press

ISBN: 1107010039

Category: Mathematics

Page: 420

View: 4277

An accessible introduction to Hilbert spaces, combining the theory with applications of Hilbert methods in signal processing.

Introduction to Banach Spaces and Algebras

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Author: Graham R. Allan,Harold G. Dales

Publisher: Oxford University Press

ISBN: 0199206538

Category: Banach algebras

Page: 371

View: 754

A graduate level text in functional analysis, with an emphasis on Banach algebras. Based on lectures given for Part III of the Cambridge Mathematical Tripos, the text will assume a familiarity with elementary real and complex analysis, and some acquaintance with metric spaces, analytic topology and normed spaces (but not theorems depending on Baire category, or any version of the Hahn-Banach theorem).

An Introduction to Nonlinear Analysis

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Author: Martin Schechter

Publisher: Cambridge University Press

ISBN: 9780521843973

Category: Mathematics

Page: 357

View: 1323

The techniques that can be used to solve non-linear problems are far different than those that are used to solve linear problems. Many courses in analysis and applied mathematics attack linear cases simply because they are easier to solve and do not require a large theoretical background in order to approach them. Professor Schechter's 2005 book is devoted to non-linear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving non-linear problems is developed whilst demonstrating their application to problems in one dimension and then leading to higher dimensions. The reader is guided using simple exposition and proof, assuming a minimal set of pre-requisites. For completion, a set of appendices covering essential basics in functional analysis and metric spaces is included, making this ideal as an accompanying text on an upper-undergraduate or graduate course, or even for self-study.

An Introduction to the Philosophy of Mathematics

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Author: Mark Colyvan

Publisher: Cambridge University Press

ISBN: 0521826020

Category: Mathematics

Page: 188

View: 6179

This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each chapter has a number of discussion questions and recommended further reading from both the contemporary literature and older sources. Very little mathematical background is assumed and all of the mathematics encountered is clearly introduced and explained using a wide variety of examples. The book is suitable for an undergraduate course in philosophy of mathematics and, more widely, for anyone interested in philosophy and mathematics.

Nonstandard Analysis and Its Applications

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Author: Nigel Cutland

Publisher: Cambridge University Press

ISBN: 052135109X

Category: Mathematics

Page: 346

View: 4557

This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topology. The book arises from a conference held in July 1986 at the University of Hull which was designed to provide both an introduction to the subject through introductory lectures, and surveys of the state of research. The first part of the book is devoted to the introductory lectures and the second part consists of presentations of applications of NSA to dynamical systems, topology, automata and orderings on words, the non- linear Boltzmann equation and integration on non-standard hulls of vector lattices. One of the book's attractions is that a standard notation is used throughout so the underlying theory is easily applied in a number of different settings. Consequently this book will be ideal for graduate students and research mathematicians coming to the subject for the first time and it will provide an attractive and stimulating account of the subject.