Spectral Theory Of Functions And Operators Ii
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Spectral Theory Of Functions And Operators
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Author : Nikolaj Kapitonovič Nikolʹskij
language : en
Publisher: American Mathematical Soc.
Release Date : 1980
Spectral Theory Of Functions And Operators written by Nikolaj Kapitonovič Nikolʹskij and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
Spectral Theory Of Functions And Operators Ii
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1980
Spectral Theory Of Functions And Operators Ii written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Analytic functions categories.
Spectral Theory Of Functions And Operators
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Author : Nikolai Kapitonovich Nikolskii
language : en
Publisher:
Release Date : 1979
Spectral Theory Of Functions And Operators written by Nikolai Kapitonovich Nikolskii and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Analytic functions categories.
Spectral Theory Of Ordinary Differential Operators
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Author : Joachim Weidmann
language : en
Publisher: Springer
Release Date : 2006-11-15
Spectral Theory Of Ordinary Differential Operators written by Joachim Weidmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating on -valued functions existence and construction of self-adjoint realizations via boundary conditions, determination and study of general properties of the resolvent, spectral representation and spectral resolution. Special attention is paid to the question of separated boundary conditions, spectral multiplicity and absolutely continuous spectrum. For the case nm=2 (Sturm-Liouville operators and Dirac systems) the classical theory of Weyl-Titchmarch is included. Oscillation theory for Sturm-Liouville operators and Dirac systems is developed and applied to the study of the essential and absolutely continuous spectrum. The results are illustrated by the explicit solution of a number of particular problems including the spectral theory one partical Schrödinger and Dirac operators with spherically symmetric potentials. The methods of proof are functionally analytic wherever possible.
Spectral Theory Of Non Self Adjoint Two Point Differential Operators
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Author : John Locker
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Spectral Theory Of Non Self Adjoint Two Point Differential Operators written by John Locker and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Develops the spectral theory of an nth order non-self-adjoint two- point differential operator L in the complex Hilbert space L2[0,1]. The differential operator L is determined by an nth order formal differential l and by n linearly independent boundary values B1,.,Bn. Locker first lays the foundations of the spectral theory for closed linear operators and Fredholm operators in Hilbert spaces before developing the spectral theory of the differential operator L. The book is a sequel to Functional analysis and two-point differential operators, 1986. Annotation copyrighted by Book News, Inc., Portland, OR.
Spectral Theory Of Linear Operators
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Author : Abram Iezekiilovich Plesner
language : en
Publisher:
Release Date : 1969
Spectral Theory Of Linear Operators written by Abram Iezekiilovich Plesner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.
Spectral Theory And Differential Operators
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Author : E. Brian Davies
language : en
Publisher: Cambridge University Press
Release Date : 1995
Spectral Theory And Differential Operators written by E. 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 Of Operators In Hilbert Space
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Author : Kurt O. Friedrichs
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Spectral Theory Of Operators In Hilbert Space written by Kurt O. Friedrichs 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.
The present lectures intend to provide an introduction to the spectral analysis of self-adjoint 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 formal aspects of these concepts are explained in the first two chapters. Only then is the notion of Hilbert space introduced. The following three chapters concern bounded, completely continuous, and non-bounded operators. Next, simple differential operators are treated as operators in Hilbert space, and the final chapter deals with the perturbation of discrete and continuous spectra. The preparation of the original version of these lecture notes was greatly helped by the assistance of P. Rejto. Various valuable suggestions made by him and by R. Lewis have been incorporated. The present version of the notes contains extensive modifica tions, in particular in the chapters on bounded and unbounded operators. February, 1973 K.O.F. PREFACE TO THE SECOND PRINTING The second printing (1980) is a basically unchanged reprint in which a number of minor errors were corrected. The author wishes to thank Klaus Schmidt (Lausanne) and John Sylvester (New York) for their lists of errors. v TABLE OF CONTENTS I. Spectral Representation 1 1. Three typical problems 1 12 2. Linear space and functional representation.
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 Of Block Operator Matrices And Applications
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Author : Christiane Tretter
language : en
Publisher: World Scientific
Release Date : 2008-10-15
Spectral Theory Of Block Operator Matrices And Applications written by Christiane Tretter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-15 with Science categories.
This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices. Particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not readily apply: non-self-adjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics. The main topics include: localization of the spectrum by means of new concepts of numerical range; investigation of the essential spectrum; variational principles and eigenvalue estimates; block diagonalization and invariant subspaces; solutions of algebraic Riccati equations; applications to spectral problems from magnetohydrodynamics, fluid mechanics, and quantum mechanics. Contents:Bounded Block Operator Matrices:The Quadratic Numerical RangeSpecial Classes of Block Operator MatricesSpectral InclusionEstimates of the ResolventCorners of the Quadratic Numerical RangeSchur Complements and Their FactorizationBlock DiagonalizationSpectral Supporting SubspacesVariational Principles for Eigenvalues in GapsJ-Self-Adjoint Block Operator MatricesThe Block Numerical RangeNumerical Ranges of Operator PolynomialsGershgorin's Theorem for Block Operator MatricesUnbounded Block Operator Matrices:Relative Boundedness and Relative CompactnessClosedness and Closability of Block Operator MatricesSpectrum and ResolventThe Essential SpectrumSpectral InclusionSymmetric and J-Symmetric Block Operator MatricesDichotomous Block Operator Matrices and Riccati EquationsBlock Diagonalization and Half Range CompletenessUniqueness Results for Solutions of Riccati EquationsVariational PrinciplesEigenvalue EstimatesApplications in Mathematical Physics:Upper Dominant Block Operator Matrices in MagnetohydrodynamicsDiagonally Dominant Block Operator Matrices in Fluid MechanicsOff-Diagonally Dominant Block Operator Matrices in Quantum Mechanics Readership: Mathematicians, physicists and engineers. Keywords:Operator Theory;Spectral Theory;Eigenvalues;Differential Equations;Riccati Equations;Numerical Range;Mathematical Physics;Matrix TheoryKey Features:Challenging spectral problems to which standard methods do not applyNew results even in the finite dimensional caseMany illustrating examplesWide range of possible applicationsReviews:“This book is a valuable addition to the literature and will be of great help for those working in this field already as well as for people looking for an interesting introduction to the topic.”Mathematical Reviews