Inverse spectral problem for analytic plane domains I: Balian-Bloch trace formula
Spectral Theory
2015-06-26 v3 Analysis of PDEs
Abstract
We give a rigorous version of the classical Balian-Bloch trace formula, a semiclassical expansion around a periodic reflecting ray of the (regularized) resolvent of the Dirichlet Laplacian on a bounded smooth plane domain. It is equivalent to the Poisson relation (or wave trace formula) between spectrum and closed geodesics. We view it primarily as a computational device for explicitly calculating wave trace invariants. Its effectiveness will be illustrated in subsquent articles in the series in which concrete inverse spectral results are proved.
Cite
@article{arxiv.math/0111077,
title = {Inverse spectral problem for analytic plane domains I: Balian-Bloch trace formula},
author = {Steve Zelditch},
journal= {arXiv preprint arXiv:math/0111077},
year = {2015}
}
Comments
First in a series on the inverse spectral problem for analytic plane domains. 53 pages, 1 figure. Added some references