B.M. Brown, M. Langer and M. Marletta,
Spectral concentrations and resonances of a second order block operator matrix and an associated λ-rational Sturm–Liouville problem,
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460 (2004), 3403–3420

Abstract:
This paper studies the resonances and points of spectral concentration of the block operator matrix

⎛ −d2/dx2+q √(tw) ⎞
⎜ ⎟
⎝ √(tw) u ⎠
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.

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