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A guide to spectral theoryapplicatio...

Cheverry, Christophe.

A guide to spectral theoryapplications and exercises /

Record Type:	Electronic resources : Monograph/item
Title/Author:	A guide to spectral theoryby Christophe Cheverry, Nicolas Raymond.
Reminder of title:	applications and exercises /
Author:	Cheverry, Christophe.
other author:	Raymond, Nicolas.
Published:	Cham :Springer International Publishing :2021.
Description:	xx, 258 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Spectral theory (Mathematics)
Online resource:	https://doi.org/10.1007/978-3-030-67462-5
ISBN:	9783030674625$q(electronic bk.)

A guide to spectral theoryapplications and exercises /
Cheverry, Christophe.

A guide to spectral theoryapplications and exercises /[electronic resource] :by Christophe Cheverry, Nicolas Raymond. - Cham :Springer International Publishing :2021. - xx, 258 p. :ill., digital ;24 cm. - Birkhauser advanced texts Basler Lehrbucher,1019-6242. - Birkhauser advanced texts Basler Lehrbucher..

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.

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.

ISBN: 9783030674625$q(electronic bk.)

Standard No.: 10.1007/978-3-030-67462-5doiSubjects--Topical Terms:

182365
Spectral theory (Mathematics)

LC Class. No.: QA320 / .C44 2021

Dewey Class. No.: 515.7222

A guide to spectral theoryapplications and exercises /
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505 0 $a 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.
520 $a 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.
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