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A sharp lower bound for a resonance-counting function in even dimensions

This paper proves sharp lower bounds on a resonance counting function for obstacle scattering in even-dimensional Euclidean space without a need for trapping assumptions. Similar lower bounds are proved for some other compactly supported perturbations of the Laplacian on even-dimensional Euclidean space, for example, for the Laplacian for certain metric perturbations. The proof uses a Poisson formula for resonances, complementary to one proved by Zworski in even dimensions.

preprint2015arXivOpen access
T. J. Christiansen
math-phmath.MPmath.SP
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T. J. Christiansen

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