Birkhäuser Advanced Texts Basler Lehrbücher

A Guide to Spectral Theory

Applications and Exercises

Authors: Cheverry, Christophe, Raymond, Nicolas

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  • Illustrates a variety of applications of spectral theory with a focus on quantum physics
  • Provides potential research directions for students and numerous references to more advanced treatments of many topics
  • Guides readers through topics using a progressive, concise approach
  • Allows instructors to easily adapt more advanced concepts to different graduate level courses
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About this Textbook

This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics.  Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book.
Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader.
A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters.

About the authors


Christophe Cheverry is a mathematics professor at the University of Rennes 1. He works in the area of analysis, partial differential equations, and mathematical physics. Nicolas Raymond is a mathematics professor at the University of Angers. His research is focused on semiclassical spectral theory and partial differential equations.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-030-67462-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA in USD
  • ISBN 978-3-030-67461-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
A Guide to Spectral Theory
Book Subtitle
Applications and Exercises
Authors
Series Title
Birkhäuser Advanced Texts Basler Lehrbücher
Copyright
2021
Publisher
Birkhäuser Basel
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-67462-5
DOI
10.1007/978-3-030-67462-5
Hardcover ISBN
978-3-030-67461-8
Series ISSN
1019-6242
Edition Number
1
Number of Pages
XX, 258
Number of Illustrations
2 b/w illustrations
Topics