English

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.

Keywords

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

R2 v1 2026-06-22T11:22:25.228Z