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Cover: 9783030674649 | A Guide to Spectral Theory | Applications and Exercises | Taschenbuch
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A Guide to Spectral Theory
Applications and Exercises
Taschenbuch von Nicolas Raymond (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
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.
Zusammenfassung

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

Inhaltsverzeichnis
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's 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.- Bibliography.- Index.
Details
Medium: Taschenbuch
Reihe: Birkhäuser Advanced Texts Basler Lehrbücher
Inhalt: xx
258 S.
2 s/w Illustr.
258 p. 2 illus.
ISBN-13: 9783030674649
ISBN-10: 3030674649
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Raymond, Nicolas
Cheverry, Christophe
Auflage: 1st ed. 2021
Hersteller: Springer International Publishing
Springer International Publishing AG
Birkhäuser Advanced Texts Basler Lehrbücher
Maße: 235 x 155 x 16 mm
Von/Mit: Nicolas Raymond (u. a.)
Erscheinungsdatum: 07.05.2022
Gewicht: 0,429 kg
Artikel-ID: 121427570
Über den Autor
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.
Zusammenfassung

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

Inhaltsverzeichnis
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's 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.- Bibliography.- Index.
Details
Medium: Taschenbuch
Reihe: Birkhäuser Advanced Texts Basler Lehrbücher
Inhalt: xx
258 S.
2 s/w Illustr.
258 p. 2 illus.
ISBN-13: 9783030674649
ISBN-10: 3030674649
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Raymond, Nicolas
Cheverry, Christophe
Auflage: 1st ed. 2021
Hersteller: Springer International Publishing
Springer International Publishing AG
Birkhäuser Advanced Texts Basler Lehrbücher
Maße: 235 x 155 x 16 mm
Von/Mit: Nicolas Raymond (u. a.)
Erscheinungsdatum: 07.05.2022
Gewicht: 0,429 kg
Artikel-ID: 121427570
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