Generic simplicity of ellipses
Spectral Theory
2024-07-22 v2
Abstract
We prove that the Laplace spectrum of the generic ellipse is simple, both with Neumann and Dirichlet boundary condition. We rely on the known multiplicities in the spectrum of the disk (Bourget's hypothesis) and on a refined version of our method of asymptotic separation of variables. In v1, the statement of prop. 2.1 is correct but the proof is not.
Keywords
Cite
@article{arxiv.2403.07377,
title = {Generic simplicity of ellipses},
author = {Luc Hillairet and Chris M. Judge},
journal= {arXiv preprint arXiv:2403.07377},
year = {2024}
}