Several complex variables and the order of growth of the resonance counting function in Euclidean scattering

We study four classes of compactly supported perturbations of the Laplacian on ℝd, d ≥ 3 odd. They are a fairly general class of black box perturbations, a class of second-order, selfadjoint, elliptic differential operators, Laplacians associated to metric perturbations, and the Dirichlet Laplacian...

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Bibliographic Details
Published in:International Mathematics Research Notices 2006, Vol.2006 (25)
Main Author: Christiansen, T. J.
Format: Article
Language:English
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Summary:We study four classes of compactly supported perturbations of the Laplacian on ℝd, d ≥ 3 odd. They are a fairly general class of black box perturbations, a class of second-order, selfadjoint, elliptic differential operators, Laplacians associated to metric perturbations, and the Dirichlet Laplacian on the exterior of a star-shaped obstacle. In each case, we show that generically the resonance counting function has maximal order of growth.
ISSN:1073-7928
1687-1197
1687-0247
DOI:10.1155/IMRN/2006/43160