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 0308-2105Full text not available in this repository. (Request a copy from the Strathclyde author)
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.
|Keywords:||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:||06 Jan 2017 10:20|