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Hilbert Space, Boundary Value Problems and Orthogonal Polynomials

  • Book
  • © 2002

Overview

Authors:
  1. Allan M. Krall

    1. Department of Mathematics, The Pennsylvania State University, University Park, USA

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

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About this book

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.

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Part 1

    1. Hilbert Spaces

      • Allan M. Krall
      Pages 1-16

    2. Bounded Linear Operators On a Hilbert Space

      • Allan M. Krall
      Pages 17-40

    3. Unbounded Linear Operators On a Hilbert Space

      • Allan M. Krall
      Pages 41-50
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Authors and Affiliations

  • Department of Mathematics, The Pennsylvania State University, University Park, USA

    Allan M. Krall

Bibliographic Information

  • Book Title: Hilbert Space, Boundary Value Problems and Orthogonal Polynomials

  • Authors: Allan M. Krall

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-8155-5

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2002

  • Hardcover ISBN: 978-3-7643-6701-5Published: 01 April 2002

  • Softcover ISBN: 978-3-0348-9459-3Published: 24 October 2012

  • eBook ISBN: 978-3-0348-8155-5Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XIV, 354

  • Topics: Analysis

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