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

Abstract

This paper studies the resonances and points of spectral concentration of the block operator matrix ( − d2 d x 2 +q tw tw ) in the space L2(0,1)⊕L2(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.