Overview
- 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
Part of the book series: Birkhäuser Advanced Texts Basler Lehrbücher (BAT)
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Table of contents (10 chapters)
Keywords
About this 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.
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Authors and Affiliations
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.
Bibliographic Information
Book Title: A Guide to Spectral Theory
Book Subtitle: Applications and Exercises
Authors: Christophe Cheverry, Nicolas Raymond
Series Title: Birkhäuser Advanced Texts Basler Lehrbücher
DOI: https://doi.org/10.1007/978-3-030-67462-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-67461-8Published: 07 May 2021
Softcover ISBN: 978-3-030-67464-9Published: 07 May 2022
eBook ISBN: 978-3-030-67462-5Published: 06 May 2021
Series ISSN: 1019-6242
Series E-ISSN: 2296-4894
Edition Number: 1
Number of Pages: XX, 258
Number of Illustrations: 2 b/w illustrations
Topics: Functional Analysis, Analysis, Mathematical Physics