A guide to spectral theory : applications and exercises / Christophe Cheverry, Nicolas Raymond.
Cheverry, Christophe.; Raymond, Nicolas, author.
2021
QA320
Available Online

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Title A guide to spectral theory : applications and exercises / Christophe Cheverry, Nicolas Raymond.
Author Cheverry, Christophe.
ISBN 9783030674625 (electronic bk.)
3030674622 (electronic bk.)
3030674614 (print)
9783030674618 (print)
DOI https://doi.org/10.1007/978-3-030-67462-5
Imprint Cham : Birkhäuser, 2021.
Language English
Description 1 online resource (xx, 258 pages)
Other Standard Identifiers 10.1007/978-3-030-67462-5 doi
Call Number QA320
Dewey Decimal Classification 515/.7222
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed May 11, 2021).
Added Author Raymond, Nicolas, author.
Series Birkhäuser advanced texts, 1019-6242
Available in Other Form Print version: 9783030674618
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Foreword
Prolegomena
Chapter 1: A First Look at Spectral Theory
Chapter 2: Unbounded Operators
Chapter 3: Spectrum
Chapter 4: Compact Operators
Chapter 5: Fredholm Theory
Chapter 6:Spectrum of Self-Adjoint Operators
Chapter 7: Hille-Yosida and Stone Theorems
Chapter 8: About the Spectral Measure
Chapter 9: Trace-class and Hilbert-Schmidt Operators
Chapter 10: Selected Applications of the Functional Calculus
Appendix A: Reminders of Functional Analysis.

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