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Hilbert Space, Boundary Value Problems and Orthogonal Polynomials

  • Allan M. Krall

Part of the Operator Theory: Advances and Applications book series (OT, volume 133)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Part 1

    1. Allan M. Krall
      Pages 1-16
    2. Allan M. Krall
      Pages 17-40
  3. Part 2

  4. Part 3

  5. Back Matter
    Pages 343-352

About this book

Introduction

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.

Keywords

Boundary value problem Differential equations Hilbert space differential equation orthogonal polynomials orthogonal poynomials

Authors and affiliations

  • Allan M. Krall
    • 1
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

Bibliographic information

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