Hilbert Space Boundary Value Problems And Orthogonal Polynomials
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Hilbert Space Boundary Value Problems And Orthogonal Polynomials
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Author : Allan M. Krall
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Hilbert Space Boundary Value Problems And Orthogonal Polynomials written by Allan M. Krall 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.
The following tract is divided into three parts: Hilbert spaces and their (bounded and unbounded) self-adjoint operators, linear Hamiltonian systemsand their scalar counterparts and their application to orthogonal polynomials. In a sense, this is an updating of E. C. Titchmarsh's classic Eigenfunction Expansions. My interest in these areas began in 1960-61, when, as a graduate student, I was introduced by my advisors E. J. McShane and Marvin Rosenblum to the ideas of Hilbert space. The next year I was given a problem by Marvin Rosenblum that involved a differential operator with an "integral" boundary condition. That same year I attended a class given by the Physics Department in which the lecturer discussed the theory of Schwarz distributions and Titchmarsh's theory of singular Sturm-Liouville boundary value problems. I think a Professor Smith was the in structor, but memory fails. Nonetheless, I am deeply indebted to him, because, as we shall see, these topics are fundamental to what follows. I am also deeply indebted to others. First F. V. Atkinson stands as a giant in the field. W. N. Everitt does likewise. These two were very encouraging to me during my younger (and later) years. They did things "right." It was a revelation to read the book and papers by Professor Atkinson and the many fine fundamen tal papers by Professor Everitt. They are held in highest esteem, and are given profound thanks.
Boundary Value Problems And Orthogonal Expansions
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Author : C. R. MacCluer
language : en
Publisher: Institute of Electrical & Electronics Engineers(IEEE)
Release Date : 1994
Boundary Value Problems And Orthogonal Expansions written by C. R. MacCluer and has been published by Institute of Electrical & Electronics Engineers(IEEE) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
For a first course in the topic using the modern, norm-based Sobolev techniques not currently available in published format. Major concepts are presented with minimal possible detail and details are pushed into the exercises, omitted, or postponed until later sections. Includes worked examples of pr
Second Order Sturm Liouville Difference Equations And Orthogonal Polynomials
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Author : Alouf Jirari
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Second Order Sturm Liouville Difference Equations And Orthogonal Polynomials written by Alouf Jirari 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 1995 with Mathematics categories.
This well-written book is a timely and significant contribution to the understanding of difference equations. Presenting machinery for analyzing many discrete physical situations, the book will be of interest to physicists and engineers as well as mathematicians. The book develops a theory for regular and singular Sturm-Liouville boundary value problems for difference equations, generalizing many of the known results for differential equations. Discussing the self-adjointness of these problems as well as their abstract spectral resolution in the appropriate $L^2$ setting, the book gives necessary and sufficient conditions for a second-order difference operator to be self-adjoint and have orthogonal polynomials as eigenfunctions. These polynomials are classified into four categories, each of which is given a properties survey and a representative example. Finally, the book shows that the various difference operators defined for these problems are still self-adjoint when restricted to ``energy norms''. This book is suitable as a text for an advanced graduate course on Sturm-Liouville operators or on applied analysis.
Boundary Value Problems And Fourier Expansions
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Author : Charles R. MacCluer
language : en
Publisher: Courier Corporation
Release Date : 2013-01-18
Boundary Value Problems And Fourier Expansions written by Charles R. MacCluer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-18 with Mathematics categories.
Based on modern Sobolev methods, this text integrates numerical methods and symbolic manipulation into an elegant viewpoint that is consonant with implementation by digital computer. 2004 edition. Includes 64 figures. Exercises.
Boundary Value Problems And Markov Processes
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Author : Kazuaki Taira
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-30
Boundary Value Problems And Markov Processes written by Kazuaki Taira 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 2009-06-30 with Mathematics categories.
This is a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel’ boundary conditions in probability theory. It presents new developments in the theory of singular integrals.
Introductory Functional Analysis
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Author : B.D. Reddy
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Introductory Functional Analysis written by B.D. Reddy 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 2013-11-27 with Mathematics categories.
Providing an introduction to functional analysis, this text treats in detail its application to boundary-value problems and finite elements, and is distinguished by the fact that abstract concepts are motivated and illustrated wherever possible. It is intended for use by senior undergraduates and graduates in mathematics, the physical sciences and engineering, who may not have been exposed to the conventional prerequisites for a course in functional analysis, such as real analysis. Mature researchers wishing to learn the basic ideas of functional analysis will equally find this useful. Offers a good grounding in those aspects of functional analysis which are most relevant to a proper understanding and appreciation of the mathematical aspects of boundary-value problems and the finite element method.
Topics In Interpolation Theory
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Author : Harry Dym
language : en
Publisher: Springer Science & Business Media
Release Date : 1997
Topics In Interpolation Theory written by Harry Dym 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 1997 with Mathematics categories.
Vladimir Petrovich Potapov, as remembered by colleagues, friends and former students.- On a minimum problem in function theory and the number of roots of an algebraic equation inside the unit disc.- On tangential interpolation in reproducing kernel Hilbert modules and applications.- Notes on a Nevanlinna-Pick interpolation problem for generalized Nevanlinna functions.- The indefinite metric in the Schur interpolation problem for analytic functions, IV.- Bitangential interpolation for upper triangular operators.- Bitangential interpolation for upper triangular operators when the Pick operator is strictly positive.- Integral representations of a pair of nonnegative operators and interpolation problems in the Stieltjes class.- On recovering a multiplicative integral from its modulus.- On Schur functions and Szegö orthogonal polynomials.- Hilbert spaces of entire functions as a J theory subject.- On transformations of Potapov's fundamental matrix inequality.- An abstract interpolation problem and the extension theory of isometric operators.- On the theory of matrix-valued functions belonging to the Smirnov class.- Integral representation of function of class Ka.- On the theory of entire matrix-functions of exponential type.- Analogs of Nehari and Sarason theorems for character-automorphic functions and some related questions.- The Blaschke-Potapov factorization theorem and the theory of nonselfadjoint operators.- Weyl matrix circles as a tool for uniqueness in the theory of multiplicative representation of J-inner functions.- On a criterion of positive definiteness.- Matrix boundary value problems with eigenvalue dependent boundary conditions (The linear case).- Weyl-Titchmarsh functions of the canonical periodical system of differential equations.- On boundary values of functions regular in a disk.
Hilbert Space Methods For Partial Differential Equations
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Author : Ralph E. Showalter
language : en
Publisher: Pitman Publishing
Release Date : 1979
Hilbert Space Methods For Partial Differential Equations written by Ralph E. Showalter and has been published by Pitman Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
Course In Analysis A Vol Iv Fourier Analysis Ordinary Differential Equations Calculus Of Variations
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Author : Niels Jacob
language : en
Publisher: World Scientific
Release Date : 2018-07-19
Course In Analysis A Vol Iv Fourier Analysis Ordinary Differential Equations Calculus Of Variations written by Niels Jacob and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-19 with Mathematics categories.
In the part on Fourier analysis, we discuss pointwise convergence results, summability methods and, of course, convergence in the quadratic mean of Fourier series. More advanced topics include a first discussion of Hardy spaces. We also spend some time handling general orthogonal series expansions, in particular, related to orthogonal polynomials. Then we switch to the Fourier integral, i.e. the Fourier transform in Schwartz space, as well as in some Lebesgue spaces or of measures.Our treatment of ordinary differential equations starts with a discussion of some classical methods to obtain explicit integrals, followed by the existence theorems of Picard-Lindelöf and Peano which are proved by fixed point arguments. Linear systems are treated in great detail and we start a first discussion on boundary value problems. In particular, we look at Sturm-Liouville problems and orthogonal expansions. We also handle the hypergeometric differential equations (using complex methods) and their relations to special functions in mathematical physics. Some qualitative aspects are treated too, e.g. stability results (Ljapunov functions), phase diagrams, or flows.Our introduction to the calculus of variations includes a discussion of the Euler-Lagrange equations, the Legendre theory of necessary and sufficient conditions, and aspects of the Hamilton-Jacobi theory. Related first order partial differential equations are treated in more detail.The text serves as a companion to lecture courses, and it is also suitable for self-study. The text is complemented by ca. 260 problems with detailed solutions.
Functional Analysis And Boundary Value Problems
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Author : B. Dayanand Reddy
language : en
Publisher: Longman Scientific and Technical
Release Date : 1986
Functional Analysis And Boundary Value Problems written by B. Dayanand Reddy and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.