Counting the Resonances in High and Even Dimensional Obstacle Scattering
Functional Analysis
2011-05-26 v1
Abstract
In this paper, we give a polynomial lower bound for the resonances of perturbed by an obstacle in even-dimensional Euclidean spaces, . The proof is based on a Poisson Summation Formula which comes from the Hadamard factorization theorem in the open upper complex plane. We take advantage of the singularity of regularized wave trace to give the pole/resonance counting function over the principal branch of logarithmic plane a lower bound.
Keywords
Cite
@article{arxiv.1105.4972,
title = {Counting the Resonances in High and Even Dimensional Obstacle Scattering},
author = {Lung-Hui Chen},
journal= {arXiv preprint arXiv:1105.4972},
year = {2011}
}