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Resonances of a λ-rational Sturm–Liouville problem

Langer, Matthias (2001) Resonances of a λ-rational Sturm–Liouville problem. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 131 (3). pp. 709-720. ISSN 0308-2105

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Abstract

We consider a family of self-adjoint 2 × 2-block operator matrices Ã_\theta in the space L_2(0,1) \oplus L_2(0,1), depending on the real parameter \theta. If Ã_0 has an eigenvalue that is embedded in the essential spectrum, then it is shown that for \theta ≠ 0 this eigenvalue in general disappears, but the resolvent of Ã_\theta has a pole on the unphysical sheet of the Riemann surface. Such a pole is called a resonance pole. The unphysical sheet arises from analytic continuation from the upper half-plane C^+ across the essential spectrum. Furthermore, the asymptotic behaviour of this resonance pole for small \theta is investigated. The results are proved by considering a certain λ-rational Sturm–Liouville problem and its Titchmarsh–Weyl coefficient.

Item type: Article
ID code: 35432
Keywords: Sturm–Liouville problem, Titchmarsh–Weyl coefficient, analytic continuation, Mathematics, Mathematics(all)
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Pure Administrator
    Date Deposited: 04 Nov 2011 15:24
    Last modified: 05 Sep 2014 13:11
    URI: http://strathprints.strath.ac.uk/id/eprint/35432

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