Regular Extensions Of Hermitian Operators

DOWNLOAD

Download Regular Extensions Of Hermitian Operators PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Regular Extensions Of Hermitian Operators book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Regular Extensions Of Hermitian Operators

DOWNLOAD
Author : A. V. Kuzhel
language : en
Publisher: VSP
Release Date : 1998-01-01

Regular Extensions Of Hermitian Operators written by A. V. Kuzhel and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Science categories.

The concept of regular extensions of an Hermitian (non-densely defined) operator was introduced by A. Kuzhel in 1980. This concept is a natural generalization of proper extensions of symmetric (densely defined) operators. The use of regular extensions enables one to study various classes of extensions of Hermitian operators without using the method of linear relations. The central question in this monograph is to what extent the Hermitian part of a linear operator determines its properties. Various properties are investigated and some applications of the theory are given. Chapter 1 deals with some results from operator theory and the theory of extensions. Chapter 2 is devoted to the investigation of regular extensions of Hermitian (symmetric) operators with certain restrictions. In chapter 3 regular extensions of Hermitian operators with the use of boundary-value spaces are investigated. In the final chapter, the results from chapters 1-3 are applied to the investigation of quasi-differential operators and models of zero-range potential with internal structure.

Regular Extensions Of Hermitian Operators

DOWNLOAD
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".

Self Adjoint Extension Schemes And Modern Applications To Quantum Hamiltonians

DOWNLOAD
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

DOWNLOAD
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.

Introduction To The Spectral Theory Of Operators In Spaces With An Indefinite Metric

DOWNLOAD
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

DOWNLOAD
Author : Fabio Bagarello
language : en
Publisher: John Wiley & Sons
Release Date : 2015-07-24

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 2015-07-24 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.

Spectral Analysis Of Differential Operators

DOWNLOAD
Author : Fedor S. Rofe-Beketov
language : en
Publisher: World Scientific
Release Date : 2005

Spectral Analysis Of Differential Operators written by Fedor S. Rofe-Beketov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic SchrAdinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals). The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators."

Analytic Methods Of Spectral Representations Of Non Selfadjoint Non Unitary Operators

DOWNLOAD
Author : Vladimir A. Zolotarev
language : en
Publisher: Springer Nature
Release Date : 2025-05-03

Analytic Methods Of Spectral Representations Of Non Selfadjoint Non Unitary Operators written by Vladimir A. Zolotarev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-03 with Mathematics categories.

This book is concerned with the theory of model representations of linear non-selfadjoint and non-unitary operators. This booming area of functional analysis owes its origins to the fundamental works of M. S. Livšic on the theory of characteristic functions, the deep studies of B. S.-Nagy and C. Foias on dilation theory, and also to the Lax–Phillips scattering theory. Here, a uniform conceptual approach is developed which organically unites all these theories. New analytic methods are introduced which make it possible to solve some important problems from the theory of spectral representations. Aimed at specialists in functional analysis, the book will also be accessible to senior mathematics students.

Modern Analysis And Applications

DOWNLOAD
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.

Operator Theory And Interpolation

DOWNLOAD
Author : Hari Bercovic
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Operator Theory And Interpolation written by Hari Bercovic 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.

Systems and control theories use sophisticated operator theoretical methods. They also provide new ideas and problems in operator theory. As a consequence, the biannual MTNS (Mathematical Theory of Networks and Systems) conference is attended by many operator theorists. At the initiative of J.W. Helton and I. Gohberg, an International Workshop on Operator Theory and Applications (IWOTA) has been organized since the early 80s, as a satellite of MTNS. The articles in this volume originated from the IWOTA conference held at Indiana University, Bloomington, in June 1996. They represent most of the areas that were discussed at the workshop with some emphasis on modern interpolation theory, a topic which has seen much progress in recent years. The contributions were, as usual, subject to a thorough refereeing process and will bring the reader to the forefront of current research in this area.