Spectral concentrations and resonances of a second order block operator matrix and an associated λ-rational Sturm-Liouville problem

Brown, B.Malcolm and Langer, M. and Marletta, Marco (2004) Spectral concentrations and resonances of a second order block operator matrix and an associated λ-rational Sturm-Liouville problem. Proceedings A: Mathematical, Physical and Engineering Sciences, 460 (2052). pp. 3403-3420. ISSN 1471-2962

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Abstract

This paper studies the resonances and points of spectral concentration of the block operator matrix $$\egin{pmatrix} -\frac{d^2}{d x^2}+q & \sqrt{tw} \\ \sqrt{tw} & u \end{pmatrix} $$ in the space $L^2(0,1) \oplus L^2(0,1)$. In particular we study the dynamics of the resonance/eigenvalue λ(t), showing that an embedded eigenvalue can evolve into a resonance and that eigenvalues which are absorbed by the essential spectrum give rise to resonance points. A connection is also established between resonances and points of spectral concentration. Finally, some numerical examples are given which show that each of the above theoretical possibilities can be realized.

Creators(s): Brown, B.Malcolm, Langer, M. ORCID logoORCID: https://orcid.org/0000-0001-8813-7914 and Marletta, Marco;
Item type:Article
ID code:2169
Keywords:resonance, spectral concentration, embedded eigenvalue, block operator matrix, λ-rational eigenvalue problem, Mathematics, Physics and Astronomy(all), Engineering(all), Mathematics(all)
Subjects:Science > Mathematics
Department:Faculty of Science > Mathematics and Statistics
Depositing user: Strathprints Administrator
Date deposited:04 Jan 2007
Last modified:20 Jan 2021 17:00
URI:https://strathprints.strath.ac.uk/id/eprint/2169
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