Author: A. V. Kuzhel
Publisher: VSP
ISBN: 9789067642941
Category : Science
Languages : en
Pages : 288
Get Book Here
Book Description
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.
Author: Israel Gohberg
Publisher: Birkhäuser
ISBN: 3034889100
Category : Mathematics
Languages : en
Pages : 269
Get Book Here
Book Description
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.
Author: I. S. Iohvidov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3112735994
Category : Mathematics
Languages : en
Pages : 120
Get Book Here
Book Description
No detailed description available for "Introduction to the Spectral Theory of Operators in Spaces with an Indefinite Metric".
Author: Fedor S. Rofe-Beketov
Publisher: World Scientific
ISBN: 9812562761
Category : Science
Languages : en
Pages : 463
Get Book Here
Book Description
- Detailed bibliographical comments and some open questions are given after each chapter - Indicates connections between the content of the book and many other topics in mathematics and physics - Open questions are formulated and commented with the intention to attract attention of young mathematicians
Author: T. Ando
Publisher: Birkhäuser
ISBN: 3034886063
Category : Science
Languages : en
Pages : 417
Get Book Here
Book Description
Author: Matteo Gallone
Publisher: Springer Nature
ISBN: 303110885X
Category : Science
Languages : en
Pages : 557
Get Book Here
Book Description
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.
Author: Hari Bercovic
Publisher: Birkhäuser
ISBN: 3034884222
Category : Mathematics
Languages : en
Pages : 311
Get Book Here
Book Description
A collection of articles emphasizing modern interpolation theory, a topic which has seen much progress in recent years. These ideas and problems in operator theory, often arising from systems and control theories, bring the reader to the forefront of current research in this area.
Author: Vadim Adamyan
Publisher: Springer Science & Business Media
ISBN: 3764399198
Category : Mathematics
Languages : en
Pages : 497
Get Book Here
Book Description
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.
Author:
Publisher:
ISBN:
Category : Operator theory
Languages : en
Pages : 652
Get Book Here
Book Description
Author: Valentina Gorbachuk
Publisher: Birkhäuser
ISBN: 303488902X
Category : Mathematics
Languages : en
Pages : 228
Get Book Here
Book Description
This book is devoted to the theory of entire Hermitian operators, an important branch of functional analysis harmoniously combining the methods of operator theory and the theory of analytic functions. This theory anables various problems of classical and modern analysis to be looked at from a uniform point of view. In addition, it serves as a source for setting and solving many new problems in both theories. The three chapters of the book are based on the notes written by his students of M. G. Krein's lectures on the theory of entire operators with (1,1) deficiency index which he delivered in 1961 at the Pedagogical Institute of Odessa, and on his works on the extension theory of Hermitian operators and the theory of analytic functions. The theory is further developed in the direction of solving the problems set up by Krein at ICM-66 in the first two appendices. The first concerns the case of Hermitian operators with arbitrary defect numbers, entire with respect to an ordinary gauge and to a generalized one as well. The other focuses on the entire operators representable by differential operators. The third appendix is the translation from Russian of the unpublished notes of Krein's lecture in which, in particular, the place of the theory of entire operators in the whole analysis is elucidated. In Krein's mathematical heritage the theory of entire operators occupies a special position.
