Expansions In Eigenfunctions Of Selfadjoint Operators
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Expansions In Eigenfunctions Of Selfadjoint Operators
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Author : I͡Uriĭ Makarovich Berezanskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 1968
Expansions In Eigenfunctions Of Selfadjoint Operators written by I͡Uriĭ Makarovich Berezanskiĭ 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 1968 with Boundary value problems categories.
Expansions In Eigenfunctions Of Selfadjoint Operators
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Author :
language : en
Publisher:
Release Date : 1968
Expansions In Eigenfunctions Of Selfadjoint Operators written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Boundary value problems categories.
Expansions In Eigenfunctions Of Selfadjoint Operators Selfadjoint Operators
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Author : John Rose
language : en
Publisher:
Release Date : 1968
Expansions In Eigenfunctions Of Selfadjoint Operators Selfadjoint Operators written by John Rose 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.
Expansions In Eigenfunctions Of Selfadjoint Operators
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Author :
language : en
Publisher:
Release Date : 1968
Expansions In Eigenfunctions Of Selfadjoint Operators written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Boundary value problems categories.
Spectral Methods In Infinite Dimensional Analysis 2 1995
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Author : I︠U︡riĭ Makarovich Berezanskiĭ
language : en
Publisher: Springer Science & Business Media
Release Date : 1995
Spectral Methods In Infinite Dimensional Analysis 2 1995 written by I︠U︡riĭ Makarovich Berezanskiĭ 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 1995 with Degree of freedom categories.
Expansions In Eigenfunctions Of Selfadjoint Operators
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Author :
language : en
Publisher:
Release Date : 1968
Expansions In Eigenfunctions Of Selfadjoint Operators written by 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.
Non Self Adjoint Schr Dinger Operator With A Periodic Potential
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Author : Oktay Veliev
language : en
Publisher: Springer Nature
Release Date : 2025-08-03
Non Self Adjoint Schr Dinger Operator With A Periodic Potential written by Oktay Veliev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-03 with Science categories.
This book offers a comprehensive exploration of spectral theory for non-self-adjoint differential operators with complex-valued periodic coefficients, addressing one of the most challenging problems in mathematical physics and quantum mechanics: constructing spectral expansions in the absence of a general spectral theorem. It examines scalar and vector Schrödinger operators, including those with PT-symmetric periodic optical potentials, and extends these methodologies to higher-order operators with periodic matrix coefficients. The second edition significantly expands upon the first by introducing two new chapters that provide a complete description of the spectral theory of non-self-adjoint differential operators with periodic coefficients. The first of these new chapters focuses on the vector case, offering a detailed analysis of the spectral theory of non-self-adjoint Schrödinger operators with periodic matrix potentials. It thoroughly examines eigenvalues, eigenfunctions, and spectral expansions for systems of one-dimensional Schrödinger operators. The second chapter develops a comprehensive spectral theory for all ordinary differential operators, including higher-order and vector cases, with periodic coefficients. It also includes a complete classification of the spectrum for PT-symmetric periodic differential operators, making this edition the most comprehensive treatment of these topics to date. The book begins with foundational topics, including spectral theory for Schrödinger operators with complex-valued periodic potentials, and systematically advances to specialized cases such as the Mathieu–Schrödinger operator and PT-symmetric periodic systems. By progressively increasing the complexity, it provides a unified and accessible framework for students and researchers. The approaches developed here open new horizons for spectral analysis, particularly in the context of optics, quantum mechanics, and mathematical physics.
Non Self Adjoint Boundary Eigenvalue Problems
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Author : R. Mennicken
language : en
Publisher: Elsevier
Release Date : 2003-06-26
Non Self Adjoint Boundary Eigenvalue Problems written by R. Mennicken and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-26 with Mathematics categories.
This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations.In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every n-th order differential equation is equivalentto a first order system, the main techniques are developed for systems. Asymptotic fundamentalsystems are derived for a large class of systems of differential equations. Together with boundaryconditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10.The contour integral method and estimates of the resolvent are used to prove expansion theorems.For Stone regular problems, not all functions are expandable, and again relatively easy verifiableconditions are given, in terms of auxiliary boundary conditions, for functions to be expandable.Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such asthe Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated.Key features:• Expansion Theorems for Ordinary Differential Equations • Discusses Applications to Problems from Physics and Engineering • Thorough Investigation of Asymptotic Fundamental Matrices and Systems • Provides a Comprehensive Treatment • Uses the Contour Integral Method • Represents the Problems as Bounded Operators • Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions
Lectures On Operator Theory And Its Applications
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Author : Albrecht Böttcher
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Lectures On Operator Theory And Its Applications written by Albrecht Böttcher 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 1996 with Mathematics categories.
Much of the importance of mathematics lies in its ability to provide theories which are useful in widely different fields of endeavour. A good example is the large and amorphous body of knowledge known as the theory of linear operators or operator theory, which came to life about a century ago as a theory to encompass properties common to matrix, differential, and integral operators. Thus, it is a primary purpose of operator theory to provide a coherent body of knowledge which can explain phenomena common to the enormous variety of problems in which such linear operators play a part. The theory is a vital part of functional analysis, whose methods and techniques are one of the major advances of twentieth century mathematics and now play a pervasive role in the modeling of phenomena in probability, imaging, signal processing, systems theory, etc, as well as in the more traditional areas of theoretical physics and mechanics. This book is based on lectures presented at a meeting on operator theory and its applications held at the Fields Institute in 1994.
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.