From quasimodes to resonances. (English) Zbl 0913.35101

Stefanov and Vodev obtained a remarkable result which says that for scattering by compactly supported perturbations in odd dimensional Euclidean space, existence of localized quasimodes implies existence of resonances rapidly converging to the real axis. The purpose of this note is to extend this result to all dimensions and to a wide class of non-compactly supported perturbations. Our method also gives lower bounds for the number of resonances in small neighbourhoods of the real axis.


35P25 Scattering theory for PDEs
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