Graduate Texts in Mathematics

Spectral Theory

Basic Concepts and Applications

Authors: Borthwick, David

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  • Offers a concise introduction to spectral theory designed for newcomers to functional analysis
  • Illustrates a variety of applications of spectral theory to differential operators, including the Dirichlet Laplacian and Schrödinger operators
  • Incorporates a brief introduction to functional analysis, with a focus on unbounded operators and separable Hilbert spaces
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eBook $29.99
$59.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-030-38002-1
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  • Immediate eBook download after purchase
Hardcover $37.99
$74.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-030-38001-4
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  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover n/a
About this Textbook

This textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis. Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature.

Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, Schrödinger operators, operators on graphs, and the spectral theory of Riemannian manifolds.

Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit specific interests within a one-semester course.


About the authors

David Borthwick is Professor and Director of Graduate Studies in the Department of Mathematics at Emory University, Georgia, USA. His research interests are in spectral theory, global and geometric analysis, and mathematical physics. His monograph  Spectral Theory of Infinite-Area Hyperbolic Surfaces appears in Birkhäuser’s Progress in Mathematics, and his Introduction to Partial Differential Equations is published in Universitext.

Reviews

“This is an excellent textbook, which shall be a very useful tool for anyone who is oriented to the applications of functional analysis, especially to partial differential equations.” (Panagiotis Koumantos, zbMATH 1444.47001, 2020)


Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $29.99
$59.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-030-38002-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $37.99
$74.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-030-38001-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover n/a
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Bibliographic Information

Bibliographic Information
Book Title
Spectral Theory
Book Subtitle
Basic Concepts and Applications
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
284
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-38002-1
DOI
10.1007/978-3-030-38002-1
Hardcover ISBN
978-3-030-38001-4
Softcover ISBN
978-3-030-38004-5
Series ISSN
0072-5285
Edition Number
1
Number of Pages
X, 338
Number of Illustrations
1 b/w illustrations, 30 illustrations in colour
Topics