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 (https://doi.org/10.1098/rspa.2003.1272)
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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.
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Item type: Article ID code: 2169 Dates: DateEventDecember 2004PublishedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Strathprints Administrator Date deposited: 04 Jan 2007 Last modified: 08 Apr 2024 15:34 URI: https://strathprints.strath.ac.uk/id/eprint/2169