Perturbation Of Isolated Eigenvalues Of Singular Differential Operators
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Perturbation Of Isolated Eigenvalues Of Singular Differential Operators
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Author : Kishor J Shinde
language : en
Publisher: Educreation Publishing
Release Date : 2018-06-20
Perturbation Of Isolated Eigenvalues Of Singular Differential Operators written by Kishor J Shinde and has been published by Educreation Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-20 with Education categories.
The objective of book is to investigate the results of limit circle case/limit point case of singular Sturm-Liouville differential operators about their spectrum and invariance under perturbation that arise in quantum mechanics. The studies of ordinary differential operators of any order and dimension have been motivated by the Herman Weyl's selected work on general singular ordinary differential expressions together with the development in quantum mechanics. The Sturm-Liouville differential equation is one of the particular forms of the general singular ordinary differential expression and it forms generalization of well known differential equations such as Bessel, Laguerre, Hermite and Legendre's differential equations which are found to have applications in several branches of mathematical physics.
Ordinary Differential Operators
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Author : Aiping Wang
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-11-08
Ordinary Differential Operators written by Aiping Wang 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 2019-11-08 with Education categories.
In 1910 Herman Weyl published one of the most widely quoted papers of the 20th century in Analysis, which initiated the study of singular Sturm-Liouville problems. The work on the foundations of Quantum Mechanics in the 1920s and 1930s, including the proof of the spectral theorem for unbounded self-adjoint operators in Hilbert space by von Neumann and Stone, provided some of the motivation for the study of differential operators in Hilbert space with particular emphasis on self-adjoint operators and their spectrum. Since then the topic developed in several directions and many results and applications have been obtained. In this monograph the authors summarize some of these directions discussing self-adjoint, symmetric, and dissipative operators in Hilbert and Symplectic Geometry spaces. Part I of the book covers the theory of differential and quasi-differential expressions and equations, existence and uniqueness of solutions, continuous and differentiable dependence on initial data, adjoint expressions, the Lagrange Identity, minimal and maximal operators, etc. In Part II characterizations of the symmetric, self-adjoint, and dissipative boundary conditions are established. In particular, the authors prove the long standing Deficiency Index Conjecture. In Part III the symmetric and self-adjoint characterizations are extended to two-interval problems. These problems have solutions which have jump discontinuities in the interior of the underlying interval. These jumps may be infinite at singular interior points. Part IV is devoted to the construction of the regular Green's function. The construction presented differs from the usual one as found, for example, in the classical book by Coddington and Levinson.
Perturbation Theory For Linear Operators
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Author : Tosio Kato
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Perturbation Theory For Linear Operators written by Tosio Kato 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 2013-06-29 with Mathematics categories.
Singular Perturbations Of Differential Operators
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Author : Sergio Albeverio
language : en
Publisher: Cambridge University Press
Release Date : 2000-03-13
Singular Perturbations Of Differential Operators written by Sergio Albeverio and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-13 with Mathematics categories.
Differential (and more general self-adjoint) operators involving singular interactions arise naturally in a range of topics such as, classical and quantum physics, chemistry, and electronics. This book presents a systematic mathematical study of these operators, with particular emphasis on spectral and scattering problems. Suitable for researchers in analysis or mathematical physics, this book could also be used as a text for an advanced course on the applications of analysis.
Acta Physica Slovaca
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Author :
language : en
Publisher:
Release Date : 1978
Acta Physica Slovaca written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Physics categories.
Sturm Liouville Operators Their Spectral Theory And Some Applications
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Author : Fritz Gesztesy
language : en
Publisher: American Mathematical Society
Release Date : 2024-09-24
Sturm Liouville Operators Their Spectral Theory And Some Applications written by Fritz Gesztesy and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-24 with Mathematics categories.
This book provides a detailed treatment of the various facets of modern Sturm?Liouville theory, including such topics as Weyl?Titchmarsh theory, classical, renormalized, and perturbative oscillation theory, boundary data maps, traces and determinants for Sturm?Liouville operators, strongly singular Sturm?Liouville differential operators, generalized boundary values, and Sturm?Liouville operators with distributional coefficients. To illustrate the theory, the book develops an array of examples from Floquet theory to short-range scattering theory, higher-order KdV trace relations, elliptic and algebro-geometric finite gap potentials, reflectionless potentials and the Sodin?Yuditskii class, as well as a detailed collection of singular examples, such as the Bessel, generalized Bessel, and Jacobi operators. A set of appendices contains background on the basics of linear operators and spectral theory in Hilbert spaces, Schatten?von Neumann classes of compact operators, self-adjoint extensions of symmetric operators, including the Friedrichs and Krein?von Neumann extensions, boundary triplets for ODEs, Krein-type resolvent formulas, sesquilinear forms, Nevanlinna?Herglotz functions, and Bessel functions.
Sensitivity Uncertainty Analysis Volume 1
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Author : Dan G. Cacuci
language : en
Publisher: CRC Press
Release Date : 2003-05-28
Sensitivity Uncertainty Analysis Volume 1 written by Dan G. Cacuci and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-28 with Mathematics categories.
As computer-assisted modeling and analysis of physical processes have continued to grow and diversify, sensitivity and uncertainty analyses have become indispensable investigative scientific tools in their own right. While most techniques used for these analyses are well documented, there has yet to appear a systematic treatment of the method based on adjoint operators, which is applicable to a much wider variety of problems than methods traditionally used in control theory. This book fills that gap, focusing on the mathematical underpinnings of the Adjoint Sensitivity Analysis Procedure (ASAP) and the use of deterministically obtained sensitivities for subsequent uncertainty analysis.
Functional Analytic Methods For Partial Differential Equations
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Author : Hiroshi Fujita
language : en
Publisher: Springer
Release Date : 2006-11-14
Functional Analytic Methods For Partial Differential Equations written by Hiroshi Fujita and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Proceedings of the International Conference on Functional Analysis and Its Application in Honor of Professor Tosio Kato, July 3-6, 1989, University of Tokyo, and the Symposium on Spectral and Scattering Theory, held July 7, 1989, at Gakushin University, Tokyo.
Finite Difference Methods For Ordinary And Partial Differential Equations
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Author : Randall J. LeVeque
language : en
Publisher: SIAM
Release Date : 2007-01-01
Finite Difference Methods For Ordinary And Partial Differential Equations written by Randall J. LeVeque and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Sturm Liouville Theory
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Author : Anton Zettl
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Sturm Liouville Theory written by Anton Zettl 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 2005 with Education categories.
In 1836-1837 Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which started the subject now known as the Sturm-Liouville problem. In 1910 Hermann Weyl published an article which started the study of singular Sturm-Liouville problems. Since then, the Sturm-Liouville theory remains an intensely active field of research, with many applications in mathematics and mathematical physics. The purpose of the present book is (a) to provide a modern survey of some of the basic properties of Sturm-Liouville theory and (b) to bring the reader to the forefront of knowledge about some aspects of this theory. To use the book, only a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory are assumed. An extensive list of references and examples is provided and numerous open problems are given. The list of examples includes those classical equations and functions associated with the names of Bessel, Fourier, Heun, Ince, Jacobi, Jorgens, Latzko, Legendre, Littlewood-McLeod, Mathieu, Meissner, Morse, as well as examples associated with the harmonic oscillator and the hydrogen atom. Many special functions of applied mathematics and mathematical physics occur in these examples.