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

Self Adjoint Extensions In Quantum Mechanics

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Author : D.M. Gitman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-27

Self Adjoint Extensions In Quantum Mechanics written by D.M. Gitman 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 2012-04-27 with Science categories.

This exposition is devoted to a consistent treatment of quantization problems, based on appealing to some nontrivial items of functional analysis concerning the theory of linear operators in Hilbert spaces. The authors begin by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes to the naive treatment. It then builds the necessary mathematical background following it by the theory of self-adjoint extensions. By considering several problems such as the one-dimensional Calogero problem, the Aharonov-Bohm problem, the problem of delta-like potentials and relativistic Coulomb problemIt then shows how quantization problems associated with correct definition of observables can be treated consistently for comparatively simple quantum-mechanical systems. In the end, related problems in quantum field theory are briefly introduced. This well-organized text is most suitable for students and post graduates interested in deepening their understanding of mathematical problems in quantum mechanics. However, scientists in mathematical and theoretical physics and mathematicians will also find it useful.

Linear Operators In Hilbert Spaces

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Author : Joachim Weidmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Linear Operators In Hilbert Spaces written by Joachim Weidmann 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 English edition is almost identical to the German original Lineare Operatoren in Hilbertriiumen, published by B. G. Teubner, Stuttgart in 1976. A few proofs have been simplified, some additional exercises have been included, and a small number of new results has been added (e.g., Theorem 11.11 and Theorem 11.23). In addition a great number of minor errors has been corrected. Frankfurt, January 1980 J. Weidmann vii Preface to the German edition The purpose of this book is to give an introduction to the theory of linear operators on Hilbert spaces and then to proceed to the interesting applica tions of differential operators to mathematical physics. Besides the usual introductory courses common to both mathematicians and physicists, only a fundamental knowledge of complex analysis and of ordinary differential equations is assumed. The most important results of Lebesgue integration theory, to the extent that they are used in this book, are compiled with complete proofs in Appendix A. I hope therefore that students from the fourth semester on will be able to read this book without major difficulty. However, it might also be of some interest and use to the teaching and research mathematician or physicist, since among other things it makes easily accessible several new results of the spectral theory of differential operators.

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 Science 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.

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.

Unbounded Operator Algebras And Representation Theory

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Author : K. Schmüdgen
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 1990-12-31

Unbounded Operator Algebras And Representation Theory written by K. Schmüdgen and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-12-31 with Mathematics categories.

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Unbounded Self Adjoint Operators On Hilbert Space

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Author : Ellis I. Morris
language : en
Publisher: CreateSpace
Release Date : 2015-08-17

Unbounded Self Adjoint Operators On Hilbert Space written by Ellis I. Morris and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-17 with categories.

This updated and expanded second edition of the Unbounded Self-adjoint Operators on Hilbert Space: 265 (Graduate Texts in Mathematics) provides a user-friendly introduction to the subject, Taking a clear structural framework, it guides the reader through the subject's core elements. A flowing writing style combines with the use of illustrations and diagrams throughout the text to ensure the reader understands even the most complex of concepts. This succinct and enlightening overview is a required reading for all those interested in the subject . We hope you find this book useful in shaping your future career & Business. Feel free to send us your inquiries related to our publications to [email protected]

An Invitation To Unbounded Representations Of Algebras On Hilbert Space

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Author : Konrad Schmüdgen
language : en
Publisher: Springer Nature
Release Date : 2020-07-28

An Invitation To Unbounded Representations Of Algebras On Hilbert Space written by Konrad Schmüdgen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-28 with Mathematics categories.

This textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.

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.

Unbounded Self Adjoint Operators On Hilbert Space

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Author : Grace L. Marsden
language : en
Publisher: CreateSpace
Release Date : 2015-08-19

Unbounded Self Adjoint Operators On Hilbert Space written by Grace L. Marsden and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-19 with categories.

This updated and expanded second edition of the Unbounded Self-adjoint Operators on Hilbert Space provides a user-friendly introduction to the subject, Taking a clear structural framework, it guides the reader through the subject's core elements. A flowing writing style combines with the use of illustrations and diagrams throughout the text to ensure the reader understands even the most complex of concepts. This succinct and enlightening overview is a required reading for all those interested in the subject . We hope you find this book useful in shaping your future career & Business. Feel free to send us your inquiries related to our publications to [email protected] PW Publishers LTD Berlin Germany