Unbounded Self-adjoint Operators on Hilbert Space

  • Konrad Schmüdgen

Part of the Graduate Texts in Mathematics book series (GTM, volume 265)

Table of contents

  1. Front Matter
    Pages I-XX
  2. Basics of Closed Operators

    1. Front Matter
      Pages 1-1
    2. Konrad Schmüdgen
      Pages 3-23
    3. Konrad Schmüdgen
      Pages 25-36
    4. Konrad Schmüdgen
      Pages 37-57
  3. Spectral Theory

    1. Front Matter
      Pages 59-59
    2. Konrad Schmüdgen
      Pages 61-84
  4. Special Topics

    1. Front Matter
      Pages 115-115
    2. Konrad Schmüdgen
      Pages 117-135
    3. Konrad Schmüdgen
      Pages 137-164
  5. Perturbations of Self-adjointness and Spectra

    1. Front Matter
      Pages 165-165
    2. Konrad Schmüdgen
      Pages 167-187
  6. Forms and Operators

    1. Front Matter
      Pages 219-219
    2. Konrad Schmüdgen
      Pages 221-250
    3. Konrad Schmüdgen
      Pages 251-263
    4. Konrad Schmüdgen
      Pages 265-280
  7. Self-adjoint Extension Theory of Symmetric Operators

    1. Front Matter
      Pages 281-281

About this book


The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger  operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics   are treated on a text book level  accompanied by numerous illustrating examples and exercises. The main themes of the book are the following:
- Spectral integrals and  spectral decompositions of self-adjoint and normal operators
- Perturbations of self-adjointness and of spectra of self-adjoint operators
- Forms and operators
- Self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extension


Banach space Hamburger moment problem Hilbert space Perturbation of self-adjointness Schrödinger operators Self-adjoint extension theory Self-adjoint operators Spectral theory Sturm-Liouville operators

Authors and affiliations

  • Konrad Schmüdgen
    • 1
  1. 1.Dept. of MathematicsUniversity of LeipzigLeipzigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-007-4753-1
  • Copyright Information Springer Science+Business Media Dordrecht 2012
  • Publisher Name Springer, Dordrecht
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-94-007-4752-4
  • Online ISBN 978-94-007-4753-1
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • About this book
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