Resonances of a λrational Sturm–Liouville problem
Langer, Matthias (2001) Resonances of a λrational Sturm–Liouville problem. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 131 (3). pp. 709720. ISSN 03082105
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We consider a family of selfadjoint 2 × 2block 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 halfplane 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 λrational Sturm–Liouville problem and its Titchmarsh–Weyl coefficient.
ORCID iDs
Langer, Matthias ORCID: https://orcid.org/0000000188137914;

Item type: Article ID code: 35432 Dates: DateEventJune 2001PublishedKeywords: Sturm–Liouville problem, Titchmarsh–Weyl coefficient, analytic continuation, Mathematics, Mathematics(all) Subjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 04 Nov 2011 15:24 Last modified: 20 Jan 2021 19:48 URI: https://strathprints.strath.ac.uk/id/eprint/35432