Unbounded Self Adjoint Operators On Hilbert Space
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Unbounded Self Adjoint Operators On Hilbert Space
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Author : Konrad Schmüdgen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-09
Unbounded Self Adjoint Operators On Hilbert Space written by Konrad Schmüdgen 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 2012-07-09 with Mathematics categories.
The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises. The main themes of the book are the following: - Spectral integrals and spectral decompositions of self-adjoint and normal operators - Perturbations of self-adjointness and of spectra of self-adjoint operators - Forms and operators - Self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extension
Spectral Theory Of Self Adjoint Operators In Hilbert Space
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Author : Michael Sh. Birman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Spectral Theory Of Self Adjoint Operators In Hilbert Space written by Michael 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 Mathematics categories.
It isn't that they can't see the solution. It is Approach your problems from the right end that they can't see the problem. and begin with the answers. Then one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be com pletely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order" , which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Commutation Properties Of Hilbert Space Operators And Related Topics
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Author : Calvin R. Putnam
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Commutation Properties Of Hilbert Space Operators And Related Topics written by Calvin R. Putnam 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.
What could be regarded as the beginning of a theory of commutators AB - BA of operators A and B on a Hilbert space, considered as a dis cipline in itself, goes back at least to the two papers of Weyl [3] {1928} and von Neumann [2] {1931} on quantum mechanics and the commuta tion relations occurring there. Here A and B were unbounded self-adjoint operators satisfying the relation AB - BA = iI, in some appropriate sense, and the problem was that of establishing the essential uniqueness of the pair A and B. The study of commutators of bounded operators on a Hilbert space has a more recent origin, which can probably be pinpointed as the paper of Wintner [6] {1947}. An investigation of a few related topics in the subject is the main concern of this brief monograph. The ensuing work considers commuting or "almost" commuting quantities A and B, usually bounded or unbounded operators on a Hilbert space, but occasionally regarded as elements of some normed space. An attempt is made to stress the role of the commutator AB - BA, and to investigate its properties, as well as those of its components A and B when the latter are subject to various restrictions. Some applica tions of the results obtained are made to quantum mechanics, perturba tion theory, Laurent and Toeplitz operators, singular integral trans formations, and Jacobi matrices.
Stable Approximate Evaluation Of Unbounded Operators
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Author : C. W. Groetsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2007
Stable Approximate Evaluation Of Unbounded Operators written by C. W. Groetsch 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 2007 with Mathematics categories.
Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.
Product Formulas Nonlinear Semigroups And Addition Of Unbounded Operators
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Author : Paul R. Chernoff
language : en
Publisher: American Mathematical Soc.
Release Date : 1974
Product Formulas Nonlinear Semigroups And Addition Of Unbounded Operators written by Paul R. Chernoff 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 1974 with Mathematics categories.
This work deals with the general theory, both linear and non-linear, of operator semigroup product formulas of the type lim [over] n[right arrow][infinity] F(t/n) [superscript]n = G(t). The principal application is the use of the Trotter-Lie product formula e [superscript]tC = lim [over] n[right arrow][infinity] (e [superscript]t/nA e [superscript]t/nB) [superscript]n to define a generalized addition of semigroup generators, and self-adjoint operators in particular. The properties of generalized addition, both regular and pathological, are discussed.
Introduction To Spectral Theory In Hilbert Space
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Author : Gilbert Helmberg
language : en
Publisher: Elsevier
Release Date : 2014-11-28
Introduction To Spectral Theory In Hilbert Space written by Gilbert Helmberg and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-28 with Mathematics categories.
North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of linear operators and spectral analysis of compact linear operators, including spectral decomposition of a compact selfadjoint operator, weakly convergent sequences, spectrum of a compact linear operator, and eigenvalues of a linear operator. The manuscript ponders on the spectral analysis of bounded linear operators and unbounded selfadjoint operators. Topics include spectral decomposition of an unbounded selfadjoint operator and bounded normal operator, functions of a unitary operator, step functions of a bounded selfadjoint operator, polynomials in a bounded operator, and order relation for bounded selfadjoint operators. The publication is a valuable source of data for mathematicians and researchers interested in spectral theory in Hilbert space.
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.
Spectral Theory Of Self Adjoint Operators In Hilbert Space
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Author : M. S. Birman
language : en
Publisher:
Release Date : 1987
Spectral Theory Of Self Adjoint Operators In Hilbert Space written by M. S. Birman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Ordinary Differential Operators
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Author : Aiping Wang
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-11-08
Ordinary Differential Operators written by Aiping Wang 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 2019-11-08 with Education categories.
In 1910 Herman Weyl published one of the most widely quoted papers of the 20th century in Analysis, which initiated the study of singular Sturm-Liouville problems. The work on the foundations of Quantum Mechanics in the 1920s and 1930s, including the proof of the spectral theorem for unbounded self-adjoint operators in Hilbert space by von Neumann and Stone, provided some of the motivation for the study of differential operators in Hilbert space with particular emphasis on self-adjoint operators and their spectrum. Since then the topic developed in several directions and many results and applications have been obtained. In this monograph the authors summarize some of these directions discussing self-adjoint, symmetric, and dissipative operators in Hilbert and Symplectic Geometry spaces. Part I of the book covers the theory of differential and quasi-differential expressions and equations, existence and uniqueness of solutions, continuous and differentiable dependence on initial data, adjoint expressions, the Lagrange Identity, minimal and maximal operators, etc. In Part II characterizations of the symmetric, self-adjoint, and dissipative boundary conditions are established. In particular, the authors prove the long standing Deficiency Index Conjecture. In Part III the symmetric and self-adjoint characterizations are extended to two-interval problems. These problems have solutions which have jump discontinuities in the interior of the underlying interval. These jumps may be infinite at singular interior points. Part IV is devoted to the construction of the regular Green's function. The construction presented differs from the usual one as found, for example, in the classical book by Coddington and Levinson.
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.