A sharp lower bound for a resonance-counting function in even dimensions
Spectral Theory
2015-10-19 v1 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.1510.04952,
title = {A sharp lower bound for a resonance-counting function in even dimensions},
author = {T. J. Christiansen},
journal= {arXiv preprint arXiv:1510.04952},
year = {2015}
}
Comments
21 pages