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    Brown, B. M. Marletta, M. Naboko, S. N. and Wood, I. G. 2016. Detectable subspaces and inverse problems for Hain-Lüst-type operators. Mathematische Nachrichten, p. n/a.


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  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 131, Issue 3
  • June 2001, pp. 709-720

Resonances of a λ-rational Sturm–Liouville problem

  • Matthias Langer (a1)
  • DOI: http://dx.doi.org/10.1017/S0308210500001062
  • Published online: 01 July 2007
Abstract

We consider a family of self-adjoint 2 × 2-block operator matrices Ãϑ in the space L2(0, 1) ⊕ L2(0, 1), depending on the real parameter ϑ. If Ã0 has an eigenvalue that is embedded in the essential spectrum, then it is shown that for ϑ ≠ 0 this eigenvalue in general disappears, but the resolvent of Ãϑ 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 ϑ is investigated. The results are proved by considering a certain λ-rational Sturm–Liouville problem and its Titchmarsh–Weyl coefficient.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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