An Introduction to Hilbert Space

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Author: N. Young

Publisher: Cambridge University Press

ISBN: 9780521337175

Category: Mathematics

Page: 239

View: 7208

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 Hilbert Space

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Author: N. Young

Publisher: Cambridge University Press

ISBN: 1107717167

Category: Mathematics

Page: 256

View: 693

This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to 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. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it 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: 7881

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

Introduction to Hilbert Space

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Author: Sterling K. Berberian

Publisher: American Mathematical Soc.

ISBN: 0821819127

Category: Mathematics

Page: 206

View: 2550

Completely self-contained ... All proofs are given in full detail ... recommended for unassisted reading by beginners ... For teaching purposes this book is ideal. --Proceedings of the Edinburgh Mathematical Society The book is easy to read and, although the author had in mind graduate students, most of it is obviously appropriate for an advanced undergraduate course. It is also a book which a reasonably good student might read on his own. --Mathematical Reviews This textbook evolved from a set of course notes for first- or second-year graduate students in mathematics and related fields such as physics. It presents, in a self-contained way, various aspects of geometry and analysis of Hilbert spaces, including the spectral theorem for compact operators. Over 400 exercises provide examples and counter-examples for definitions and theorems in the book, as well as generalization of some material in the text. Aside from being an exposition of basic material on Hilbert space, this book may also serve as an introduction to other areas of functional analysis. The only prerequisite for understanding the material is a standard foundation in advanced calculus. The main notions of linear algebra, such as vector spaces, bases, etc., are explained in the first chapter of the book.

A Hilbert Space Problem Book

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Author: P.R. Halmos

Publisher: Springer Science & Business Media

ISBN: 1468493302

Category: Mathematics

Page: 373

View: 7417

From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."

Introduction to Spectral Theory in Hilbert Space

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Author: Gilbert Helmberg

Publisher: Courier Dover Publications

ISBN: 0486466221

Category: Mathematics

Page: 346

View: 4620

This text introduces students to Hilbert space and bounded self-adjoint operators, as well as the spectrum of an operator and its spectral decomposition. The author, Emeritus Professor of Mathematics at the University of Innsbruck, Austria, has ensured that the treatment is accessible to readers with no further background than a familiarity with analysis and analytic geometry. Starting with a definition of Hilbert space and its geometry, the text explores the general theory of bounded linear operators, the spectral analysis of compact linear operators, and unbounded self-adjoint operators. Extensive appendixes offer supplemental information on the graph of a linear operator and the Riemann-Stieltjes and Lebesgue integration.

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: 4960

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 Systems and Operators in Hilbert Space

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Author: Paul A. Fuhrmann

Publisher: Courier Corporation

ISBN: 0486782263

Category: Mathematics

Page: 336

View: 7260

Three-part approach, with notes and references for each section, covers linear algebra and finite dimensional systems, operators in Hilbert space, and linear systems in Hilbert space. 1981 edition.

Introduction to Operator Space Theory

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Author: Gilles Pisier

Publisher: Cambridge University Press

ISBN: 9780521811651

Category: Mathematics

Page: 478

View: 6671

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

Linear Analysis

An Introductory Course

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Author: Béla Bollobás

Publisher: Cambridge University Press

ISBN: 9780521655774

Category: Mathematics

Page: 240

View: 3099

Revised and updated introduction to functional analysis.

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: 1460

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).

Reproducing Kernel Hilbert Spaces in Probability and Statistics

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Author: Alain Berlinet,Christine Thomas-Agnan

Publisher: Springer Science & Business Media

ISBN: 1441990968

Category: Business & Economics

Page: 355

View: 5934

The book covers theoretical questions including the latest extension of the formalism, and computational issues and focuses on some of the more fruitful and promising applications, including statistical signal processing, nonparametric curve estimation, random measures, limit theorems, learning theory and some applications at the fringe between Statistics and Approximation Theory. It is geared to graduate students in Statistics, Mathematics or Engineering, or to scientists with an equivalent level.

Introduction to Hilbert Spaces with Applications

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Author: Lokenath Debnath,Piotr Mikusinski

Publisher: Elsevier

ISBN: 0080455921

Category: Mathematics

Page: 600

View: 5502

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

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: 3526

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

Foundations of Signal Processing

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Author: Martin Vetterli,Jelena Kovačević,Vivek K Goyal

Publisher: Cambridge University Press

ISBN: 1139916572

Category: Technology & Engineering

Page: N.A

View: 5912

This comprehensive and engaging textbook introduces the basic principles and techniques of signal processing, from the fundamental ideas of signals and systems theory to real-world applications. Students are introduced to the powerful foundations of modern signal processing, including the basic geometry of Hilbert space, the mathematics of Fourier transforms, and essentials of sampling, interpolation, approximation and compression The authors discuss real-world issues and hurdles to using these tools, and ways of adapting them to overcome problems of finiteness and localization, the limitations of uncertainty, and computational costs. It includes over 160 homework problems and over 220 worked examples, specifically designed to test and expand students' understanding of the fundamentals of signal processing, and is accompanied by extensive online materials designed to aid learning, including Mathematica® resources and interactive demonstrations.

Introduction to Model Spaces and their Operators

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Author: Stephan Ramon Garcia,Javad Mashreghi,William T. Ross

Publisher: Cambridge University Press

ISBN: 1316390438

Category: Mathematics

Page: N.A

View: 7636

The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.

Physical Mathematics

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Author: Kevin Cahill

Publisher: Cambridge University Press

ISBN: 1107310733

Category: Science

Page: N.A

View: 8384

Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.

Spectral Theory and Differential Operators

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Author: E. Brian Davies,Edward Brian Davies

Publisher: Cambridge University Press

ISBN: 9780521587105

Category: Mathematics

Page: 182

View: 6638

In this book, Davies introduces the reader to the theory of partial differential operators, up to the spectral theorem for bounded linear operators on Banach spaces. He also describes the theory of Fourier transforms and distributions as far as is needed to analyze the spectrum of any constant coefficient partial differential operator. He also presents a completely new proof of the spectral theorem for unbounded self-adjoint operators and demonstrates its application to a variety of second order elliptic differential operators. Finally, the book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques. Illustrated with many examples, it is well-suited to graduate-level work.

Hilbert Space

Compact Operators and the Trace Theorem

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Author: J. R. Retherford

Publisher: Cambridge University Press

ISBN: 9780521429337

Category: Mathematics

Page: 131

View: 6549

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.