## An Introduction to Hilbert Space

**Author**: N. Young

**Publisher:**Cambridge University Press

**ISBN:**9780521337175

**Category:**Mathematics

**Page:**239

**View:**9413

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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

**Author**: N. Young

**Publisher:**Cambridge University Press

**ISBN:**1107717167

**Category:**Mathematics

**Page:**256

**View:**3969

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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

**Author**: Vern I. Paulsen,Mrinal Raghupathi

**Publisher:**Cambridge University Press

**ISBN:**1107104092

**Category:**Mathematics

**Page:**192

**View:**9948

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

## Introduction to Hilbert Space

**Author**: Sterling K. Berberian

**Publisher:**American Mathematical Soc.

**ISBN:**0821819127

**Category:**Mathematics

**Page:**206

**View:**8341

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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

**Author**: P.R. Halmos

**Publisher:**Springer Science & Business Media

**ISBN:**1468493302

**Category:**Mathematics

**Page:**373

**View:**3614

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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

**Author**: Gilbert Helmberg

**Publisher:**Courier Dover Publications

**ISBN:**0486466221

**Category:**Mathematics

**Page:**346

**View:**2789

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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.

## Linear Systems and Operators in Hilbert Space

**Author**: Paul A. Fuhrmann

**Publisher:**Courier Corporation

**ISBN:**0486782263

**Category:**Mathematics

**Page:**336

**View:**5371

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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.

## A Course in Modern Mathematical Physics

*Groups, Hilbert Space and Differential Geometry*

**Author**: Peter Szekeres

**Publisher:**Cambridge University Press

**ISBN:**9780521829601

**Category:**Mathematics

**Page:**600

**View:**4128

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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.

## Reproducing Kernel Hilbert Spaces in Probability and Statistics

**Author**: Alain Berlinet,Christine Thomas-Agnan

**Publisher:**Springer Science & Business Media

**ISBN:**1441990968

**Category:**Business & Economics

**Page:**355

**View:**2733

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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.

## Linear Analysis

*An Introductory Course*

**Author**: Béla Bollobás

**Publisher:**Cambridge University Press

**ISBN:**9780521655774

**Category:**Mathematics

**Page:**240

**View:**1377

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Revised and updated introduction to functional analysis.

## Introduction to Banach Spaces and Algebras

**Author**: Graham R. Allan,Harold G. Dales

**Publisher:**Oxford University Press

**ISBN:**0199206538

**Category:**Banach algebras

**Page:**371

**View:**2965

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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).

## Introduction to Operator Space Theory

**Author**: Gilles Pisier

**Publisher:**Cambridge University Press

**ISBN:**9780521811651

**Category:**Mathematics

**Page:**478

**View:**9452

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

## Introduction to Hilbert Spaces with Applications

**Author**: Lokenath Debnath,Piotr Mikusinski

**Publisher:**Elsevier

**ISBN:**0080455921

**Category:**Mathematics

**Page:**600

**View:**2658

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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

**Author**: Rodney A. Kennedy,Parastoo Sadeghi

**Publisher:**Cambridge University Press

**ISBN:**1107010039

**Category:**Mathematics

**Page:**420

**View:**1783

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

## Physical Mathematics

**Author**: Kevin Cahill

**Publisher:**Cambridge University Press

**ISBN:**1107310733

**Category:**Science

**Page:**N.A

**View:**2780

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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.

## Introduction to Model Spaces and their Operators

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

**Publisher:**Cambridge University Press

**ISBN:**1107108748

**Category:**Mathematics

**Page:**335

**View:**7739

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A self-contained textbook which opens up this challenging field to newcomers and points to areas of future research.

## Hilbert Space

*Compact Operators and the Trace Theorem*

**Author**: J. R. Retherford

**Publisher:**Cambridge University Press

**ISBN:**9780521429337

**Category:**Mathematics

**Page:**131

**View:**1930

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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.

## Lie Groups

*An Introduction Through Linear Groups*

**Author**: Wulf Rossmann

**Publisher:**Oxford University Press on Demand

**ISBN:**9780199202515

**Category:**Mathematics

**Page:**265

**View:**3212

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Lie Groups is intended as an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analysed in detail, first with elementary matrix methods, then with the help of the structural tools typical of thetheory of semisimple groups, such as Cartan subgroups, roots, weights, and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and proceeds from there to the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.

## An Introduction to K-Theory for C*-Algebras

**Author**: M. Rørdam,Flemming Larsen,N. Laustsen

**Publisher:**Cambridge University Press

**ISBN:**9780521789448

**Category:**Mathematics

**Page:**242

**View:**5866

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This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.