A Guide To Spectral Theory
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A Guide To Spectral Theory
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Author : Christophe Cheverry
language : en
Publisher: Springer Nature
Release Date : 2021-05-06
A Guide To Spectral Theory written by Christophe Cheverry and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-06 with Mathematics categories.
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.
Spectral Theory And Differential Operators
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Author : Edward Brian Davies
language : en
Publisher: Cambridge University Press
Release Date : 1995
Spectral Theory And Differential Operators written by Edward Brian Davies and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on partial differential operators.
Spectral Theory
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Author : Edgar R. Lorch
language : en
Publisher:
Release Date : 2003-01-01
Spectral Theory written by Edgar R. Lorch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with categories.
Spectral Theory Of Operators In Hilbert Space
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Author : Kurt Otto Friedrichs
language : en
Publisher:
Release Date : 2012-07-01
Spectral Theory Of Operators In Hilbert Space written by Kurt Otto Friedrichs and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-01 with categories.
The Present Lectures Intend To Provide An Introduction To The Spectral Analysis Of Self-Joint Operators Within The Framework Of Hilbert Space Theory. The Guiding Notion In This Approach Is That Of Spectral Representation. At The Same Time The Notion Of Function Of An Operator Is Emphasized. The Definition Of Hilbert Space: In Mathematics, A Hilbert Space Is A Real Or Complex Vector Space With A Positive-Definite Hermitian Form, That Is Complete Under Its Norm. Thus It Is An Inner Product Space, Which Means That It Has Notions Of Distance And Of Angle (Especially The Notion Of Orthogonality Or Perpendicularity). The Completeness Requirement Ensures That For Infinite Dimensional Hilbert Spaces The Limits Exist When Expected, Which Facilitates Various Definitions From Calculus. A Typical Example Of A Hilbert Space Is The Space Of Square Summable Sequences. Hilbert Spaces Allow Simple Geometric Concepts, Like Projection And Change Of Basis To Be Applied To Infinite Dimensional Spaces, Such As Function Spaces. They Provide A Context With Which To Formalize And Generalize The Concepts Of The Fourier Series In Terms Of Arbitrary Orthogonal Polynomials And Of The Fourier Transform, Which Are Central Concepts From Functional Analysis. Hilbert Spaces Are Of Crucial Importance In The Mathematical Formulation Of Quantum Mechanics.
Spectral Theory
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Author : M. Sh. Birman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Spectral Theory written by M. Sh. Birman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Spectral Mapping Theorems
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Author : Robin Harte
language : en
Publisher: Springer
Release Date : 2014-04-29
Spectral Mapping Theorems written by Robin Harte and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-29 with Mathematics categories.
Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several and many variables. The basic algebraic systems – semigroups, rings and linear algebras – are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Spectral Mapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory.
Spectral Theory
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Author : Edgar Raymond Lorch
language : en
Publisher:
Release Date : 1955
Spectral Theory written by Edgar Raymond Lorch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1955 with categories.
Introduction To Spectral Theory
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Author : P. D. Hislop
language : en
Publisher:
Release Date : 1995-11-01
Introduction To Spectral Theory written by P. D. Hislop and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-01 with categories.
A Primer On Spectral Theory
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Author : Bernard Aupetit
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Primer On Spectral Theory written by Bernard Aupetit and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This textbook provides an introduction to the new techniques of subharmonic functions and analytic multifunctions in spectral theory. Topics include the basic results of functional analysis, bounded operations on Banach and Hilbert spaces, Banach algebras, and applications of spectral subharmonicity. Each chapter is followed by exercises of varying difficulty. Much of the subject matter, particularly in spectral theory, operator theory and Banach algebras, contains new results.
Spectral Theory Of Guided Waves
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Author : A.S Silbergleit
language : en
Publisher: CRC Press
Release Date : 2021-08-02
Spectral Theory Of Guided Waves written by A.S Silbergleit and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-02 with Science categories.
Spectral Theory of Guided Waves represents a distillation of the authors' (and others) efforts over several years to rigorously discuss many of the properties of guided waves. The bulk of the book deals with the properties of eigenwaves of regular waveguiding systems and relates these to a variety of physical situations and applications to illustrate their generality. The book also includes considerable discussion of the basic properties of normal waves with quadratic operator pencils. Unique in its coverage of these subjects, the book will be of interest to engineers, applied mathematicians, and physicists with a working knowledge of functional analysis and spectral theory.