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Sturm–Liouville Operators

  • Konrad Schmüdgen
Chapter
  • 4.3k Downloads
Part of the Graduate Texts in Mathematics book series (GTM, volume 265)

Abstract

Chapter 15 deals with the Hilbert space theory of Sturm–Louville operators \(-\frac{d^{2}}{dx^{2}}+ q(x)\) on intervals. First, we study the case of regular end points. Then we develop the fundamental results of H. Weyl’s classical limit point–limit circle theory. Some general limit point and limit circle criteria are proved. Next, we define boundary triplets in the various cases (regular end points, limit point case, limit circle case), determine their gamma fields and Weyl functions, and describe all self-adjoint extensions. In the final section, we derive formulas for the resolvents of some self-adjoint extensions.

Keywords

Sturm-Liouville Operators Limit Point Case Limit-circle Criteria Boundary Triplet Self-adjoint Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

Books

  1. [DS]
    Dunford, N., Schwartz, J.T.: Linear Operators, Part II. Spectral Theory. Interscience Publ., New York (1963) Google Scholar
  2. [Na2]
    Naimark, M.A.: Linear Differential Operators. Ungar, New York (1968) Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

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

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