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.
Original language | English |
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Pages (from-to) | 3403-3420 |
Number of pages | 18 |
Journal | Proceedings A: Mathematical, Physical and Engineering Sciences |
Volume | 460 |
Issue number | 2052 |
DOIs | |
Publication status | Published - Dec 2004 |
Keywords
- resonance
- spectral concentration
- embedded eigenvalue
- block operator matrix
- λ-rational eigenvalue problem