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Product Code:  GSM/226.S 
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EPUB ISBN:  9781470476618 
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MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470471927 
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Product Code:  GSM/226.S.B 
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AMS Member Price:  $136.00 $102.00 
Softcover ISBN:  9781470471927 
Product Code:  GSM/226.S 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
eBook ISBN:  9781470471910 
EPUB ISBN:  9781470476618 
Product Code:  GSM/226.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470471927 
eBook ISBN:  9781470471910 
Product Code:  GSM/226.S.B 
List Price:  $170.00 $127.50 
MAA Member Price:  $153.00 $114.75 
AMS Member Price:  $136.00 $102.00 

Book DetailsGraduate Studies in MathematicsVolume: 226; 2022; 472 ppMSC: Primary 47; 34; 35; 46
The central topic of this book is the spectral theory of bounded and unbounded selfadjoint operators on Hilbert spaces. After introducing the necessary prerequisites in measure theory and functional analysis, the exposition focuses on operator theory and especially the structure of selfadjoint operators. These can be viewed as infinitedimensional analogues of Hermitian matrices; the infinitedimensional setting leads to a richer theory which goes beyond eigenvalues and eigenvectors and studies selfadjoint operators in the language of spectral measures and the Borel functional calculus. The main approach to spectral theory adopted in the book is to present it as the interplay between three main classes of objects: selfadjoint operators, their spectral measures, and Herglotz functions, which are complex analytic functions mapping the upper halfplane to itself. Selfadjoint operators include many important classes of recurrence and differential operators; the later part of this book is dedicated to two of the most studied classes, Jacobi operators and onedimensional Schrödinger operators.
This text is intended as a course textbook or for independent reading for graduate students and advanced undergraduates. Prerequisites are linear algebra, a first course in analysis including metric spaces, and for parts of the book, basic complex analysis. Necessary results from measure theory and from the theory of Banach and Hilbert spaces are presented in the first three chapters of the book. Each chapter concludes with a number of helpful exercises.
ReadershipGraduate students and advanced undergraduates interested in functional analysis and operator theory.

Table of Contents

Chapters

Measure theory

Banach spaces

Hilbert spaces

Bounded linear operators

Bounded selfadjoint operators

Measure decompositions

Herglotz functions

Unbounded selfadjoint operators

Consequencse of the spectral theorem

Jacobi matrices

Onedimensional Schrödinger operators


Additional Material

Reviews

The book under review is aimed at beginning graduate students and advanced undergraduates. It offers a thorough and nicely presented introduction to various interesting topics in the general area of spectral theory, both classical and modern...The material is very clearly set out, and the coverage is remarkably thorough. In addition, each chapter ends with a selection of exercises, which will be useful for consolidation of the material and also for those intending to use the book as the basis of a lecture course. As a result, the book will no doubt be of real value to students and researchers alike, and it may well come to be seen as one of the standard texts on spectral theory.
David Seifert (Newcastle upon Tyne) for zbMATH 
The book is an important contribution to the applications of the spectral theorem. It allows graduate students to get acquainted with the most recent developments on Jacobi matrices and onedimensional Schrödinger operators.
Valentin Keyantuo (Universitéde FrancheComté), MathSciNet Reviews


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The central topic of this book is the spectral theory of bounded and unbounded selfadjoint operators on Hilbert spaces. After introducing the necessary prerequisites in measure theory and functional analysis, the exposition focuses on operator theory and especially the structure of selfadjoint operators. These can be viewed as infinitedimensional analogues of Hermitian matrices; the infinitedimensional setting leads to a richer theory which goes beyond eigenvalues and eigenvectors and studies selfadjoint operators in the language of spectral measures and the Borel functional calculus. The main approach to spectral theory adopted in the book is to present it as the interplay between three main classes of objects: selfadjoint operators, their spectral measures, and Herglotz functions, which are complex analytic functions mapping the upper halfplane to itself. Selfadjoint operators include many important classes of recurrence and differential operators; the later part of this book is dedicated to two of the most studied classes, Jacobi operators and onedimensional Schrödinger operators.
This text is intended as a course textbook or for independent reading for graduate students and advanced undergraduates. Prerequisites are linear algebra, a first course in analysis including metric spaces, and for parts of the book, basic complex analysis. Necessary results from measure theory and from the theory of Banach and Hilbert spaces are presented in the first three chapters of the book. Each chapter concludes with a number of helpful exercises.
Graduate students and advanced undergraduates interested in functional analysis and operator theory.

Chapters

Measure theory

Banach spaces

Hilbert spaces

Bounded linear operators

Bounded selfadjoint operators

Measure decompositions

Herglotz functions

Unbounded selfadjoint operators

Consequencse of the spectral theorem

Jacobi matrices

Onedimensional Schrödinger operators

The book under review is aimed at beginning graduate students and advanced undergraduates. It offers a thorough and nicely presented introduction to various interesting topics in the general area of spectral theory, both classical and modern...The material is very clearly set out, and the coverage is remarkably thorough. In addition, each chapter ends with a selection of exercises, which will be useful for consolidation of the material and also for those intending to use the book as the basis of a lecture course. As a result, the book will no doubt be of real value to students and researchers alike, and it may well come to be seen as one of the standard texts on spectral theory.
David Seifert (Newcastle upon Tyne) for zbMATH 
The book is an important contribution to the applications of the spectral theorem. It allows graduate students to get acquainted with the most recent developments on Jacobi matrices and onedimensional Schrödinger operators.
Valentin Keyantuo (Universitéde FrancheComté), MathSciNet Reviews