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A First Course in Spectral Theory

Milivoje Lukić Rice University, Houston, TX
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Hardcover ISBN: 978-1-4704-6656-5
Product Code: GSM/226
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AMS Member Price: $100.00 Softcover ISBN: 978-1-4704-7192-7 Product Code: GSM/226.S List Price:$85.00
MAA Member Price: $76.50 AMS Member Price:$68.00
Electronic ISBN: 978-1-4704-7191-0
Product Code: GSM/226.E
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AMS Member Price: $68.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$187.50
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AMS Member Price: $102.00 Click above image for expanded view A First Course in Spectral Theory Milivoje Lukić Rice University, Houston, TX Available Formats:  Hardcover ISBN: 978-1-4704-6656-5 Product Code: GSM/226  List Price:$125.00 MAA Member Price: $112.50 AMS Member Price:$100.00
 Softcover ISBN: 978-1-4704-7192-7 Product Code: GSM/226.S
 List Price: $85.00 MAA Member Price:$76.50 AMS Member Price: $68.00  Electronic ISBN: 978-1-4704-7191-0 Product Code: GSM/226.E  List Price:$85.00 MAA Member Price: $76.50 AMS Member Price:$68.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
 List Price: $187.50 MAA Member Price:$168.75 AMS Member Price: $150.00  List Price:$127.50 MAA Member Price: $114.75 AMS Member Price:$102.00
• Book Details

Volume: 2262022; 472 pp
MSC: Primary 47; 34; 35; 46;

The central topic of this book is the spectral theory of bounded and unbounded self-adjoint 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 self-adjoint operators. These can be viewed as infinite-dimensional analogues of Hermitian matrices; the infinite-dimensional setting leads to a richer theory which goes beyond eigenvalues and eigenvectors and studies self-adjoint 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: self-adjoint operators, their spectral measures, and Herglotz functions, which are complex analytic functions mapping the upper half-plane to itself. Self-adjoint 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 one-dimensional 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.

• Chapters
• Measure theory
• Banach spaces
• Hilbert spaces
• Bounded linear operators
• Measure decompositions
• Herglotz functions
• Consequencse of the spectral theorem
• Jacobi matrices
• One-dimensional Schrödinger operators

• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 2262022; 472 pp
MSC: Primary 47; 34; 35; 46;

The central topic of this book is the spectral theory of bounded and unbounded self-adjoint 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 self-adjoint operators. These can be viewed as infinite-dimensional analogues of Hermitian matrices; the infinite-dimensional setting leads to a richer theory which goes beyond eigenvalues and eigenvectors and studies self-adjoint 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: self-adjoint operators, their spectral measures, and Herglotz functions, which are complex analytic functions mapping the upper half-plane to itself. Self-adjoint 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 one-dimensional 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.

• Chapters
• Measure theory
• Banach spaces
• Hilbert spaces
• Bounded linear operators