Regular Extensions Of Hermitian Operators
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Regular Extensions Of Hermitian Operators
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Author : A. V. Kuzhel
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-05-18
Regular Extensions Of Hermitian Operators written by A. V. Kuzhel 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 2020-05-18 with Mathematics categories.
No detailed description available for "Regular Extensions of Hermitian Operators".
Regular Extensions Of Hermitian Operators
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Author :
language : en
Publisher: de Gruyter
Release Date : 1998-12-31
Regular Extensions Of Hermitian Operators written by and has been published by de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-31 with categories.
Fundamental Theorems On The Extension Of Hermitian Operators And Some Of Their Applications To The Theory Of Orthogonal Polynomials And To The Problem Of Moments
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Author : M. G. Krein
language : en
Publisher:
Release Date : 1968
Fundamental Theorems On The Extension Of Hermitian Operators And Some Of Their Applications To The Theory Of Orthogonal Polynomials And To The Problem Of Moments written by M. G. Krein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Presented are various theorems on the extension of operators with a systematic use of a linear-fractional transformation of a linear operator. Also shown is that every Hermitian operator with dense domain of definition which has a spectral gap admits a self-adjoint extension and preserves the gap. The invariance of defect indices in the upper and lower half planes is proven for the case of arbitrary linear operators. Fundamental concepts dealing with linear operators in a Hilbert space are presented. Various examples appear throughout the paper showing the application of the derived theorems. They are taken from the theory of orthogonal polynomials and the problem of moments. (Author).
Self Adjoint Extension Schemes And Modern Applications To Quantum Hamiltonians
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Author : Matteo Gallone
language : en
Publisher: Springer Nature
Release Date : 2023-04-04
Self Adjoint Extension Schemes And Modern Applications To Quantum Hamiltonians written by Matteo Gallone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-04 with Science categories.
This book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann and Krein–Vishik–Birman extension schemes both in their modern form and from a historical perspective, and provides a detailed analysis of a range of applications beyond the standard pedagogical examples (the latter are indexed in a final appendix for the reader’s convenience). Self-adjointness of operators on Hilbert space representing quantum observables, in particular quantum Hamiltonians, is required to ensure real-valued energy levels, unitary evolution and, more generally, a self-consistent theory. Physical heuristics often produce candidate Hamiltonians that are only symmetric: their extension to suitably larger domains of self-adjointness, when possible, amounts to declaring additional physical states the operator must act on in order to have a consistent physics, and distinct self-adjoint extensions describe different physics. Realising observables self-adjointly is the first fundamental problem of quantum-mechanical modelling. The discussed applications concern models of topical relevance in modern mathematical physics currently receiving new or renewed interest, in particular from the point of view of classifying self-adjoint realisations of certain Hamiltonians and studying their spectral and scattering properties. The analysis also addresses intermediate technical questions such as characterising the corresponding operator closures and adjoints. Applications include hydrogenoid Hamiltonians, Dirac–Coulomb Hamiltonians, models of geometric quantum confinement and transmission on degenerate Riemannian manifolds of Grushin type, and models of few-body quantum particles with zero-range interaction. Graduate students and non-expert readers will benefit from a preliminary mathematical chapter collecting all the necessary pre-requisites on symmetric and self-adjoint operators on Hilbert space (including the spectral theorem), and from a further appendix presenting the emergence from physical principles of the requirement of self-adjointness for observables in quantum mechanics.
New Results In Operator Theory And Its Applications
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Author : Israel Gohberg
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
New Results In Operator Theory And Its Applications written by Israel Gohberg and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume is dedicated to the memory of Israel Glazman, an outstanding personality and distinguished mathematician, the author of many remarkable papers and books in operator theory and its applications. The present book opens with an essay devoted to Glazman's life and scientific achievements. It focusses on the areas of his unusually wide interests and consists of 18 mathematical papers in spectral theory of differential operators and linear operators in Hilbert and Banach spaces, analytic operator functions, ordinary and partial differential equations, functional equations, mathematical physics, nonlinear functional analysis, approximation theory and optimization, and mathematical statistics. The book gives a picture of the current state of some important problems in areas of operator theory and its applications and will be of interest to a wide group of researchers working in pure and applied mathematics.
Modern Analysis And Applications
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Author : Vadim Adamyan
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-29
Modern Analysis And Applications written by Vadim Adamyan 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 2009-08-29 with Mathematics categories.
This is the first of two volumes containing peer-reviewed research and survey papers based on talks at the International Conference on Modern Analysis and Applications. The papers describe the contemporary development of subjects influenced by Mark Krein.
Introduction To The Spectral Theory Of Operators In Spaces With An Indefinite Metric
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Author : I. S. Iohvidov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 1983-01-14
Introduction To The Spectral Theory Of Operators In Spaces With An Indefinite Metric written by I. S. Iohvidov 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 1983-01-14 with Mathematics categories.
No detailed description available for "Introduction to the Spectral Theory of Operators in Spaces with an Indefinite Metric".
Non Selfadjoint Operators In Quantum Physics
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Author : Fabio Bagarello
language : en
Publisher: John Wiley & Sons
Release Date : 2015-07-20
Non Selfadjoint Operators In Quantum Physics written by Fabio Bagarello and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-20 with Science categories.
A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features: Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2000
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Conservative Realizations Of Herglotz Nevanlinna Functions
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Author : Yuri Arlinskii
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-21
Conservative Realizations Of Herglotz Nevanlinna Functions written by Yuri Arlinskii 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 2011-06-21 with Mathematics categories.
This book is devoted to conservative realizations of various classes of Stieltjes, inverse Stieltjes, and general Herglotz-Nevanlinna functions as impedance functions of linear systems. The main feature of the monograph is a new approach to the realization theory profoundly involving developed extension theory in triplets of rigged Hilbert spaces and unbounded operators as state-space operators of linear systems. The connections of the realization theory to systems with accretive, sectorial, and contractive state-space operators as well as to the Phillips-Kato sectorial extension problem, the Krein-von Neumann and Friedrichs extremal extensions are provided. Among other results the book contains applications to the inverse problems for linear systems with non-self-adjoint Schrödinger operators, Jacobi matrices, and to the Nevanlinna-Pick system interpolation.