English

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 Δ-\Delta perturbed by an obstacle in even-dimensional Euclidean spaces, n4n\geq4. 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}
}