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Spectral Theory of Sturm-Liouville Operators Approximation by Regular Problems

In: Sturm-Liouville Theory

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  • Joachim Weidmann

    (Johann Wolfgang Goethe Universität, Fachbereich Mathematik)

Abstract

It is the aim of this article to present a brief overview of the theory of Sturm-Liouville operators, self-adjointness and spectral theory: minimal and maximal operators, Weyl’s alternative (limit point/limit circle case), deficiency indices, self-adjoint realizations, spectral representation. The main part of the lecture will be devoted to the method of proving spectral results by approximating singular problems by regular problems: calculation/approximation of the discrete spectrum as well as the study of the absolutely continuous spectrum. For simplicity, most results will be presented only for the case where one end point is regular, but they can be extended to the general case, as well as to Dirac systems, to discrete operators, and (partially) to ordinary differential operators of arbitrary order.

Suggested Citation

  • Joachim Weidmann, 2005. "Spectral Theory of Sturm-Liouville Operators Approximation by Regular Problems," Springer Books, in: Werner O. Amrein & Andreas M. Hinz & David P. Pearson (ed.), Sturm-Liouville Theory, pages 75-98, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7643-7359-7_4
    DOI: 10.1007/3-7643-7359-8_4
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