Singular Bohr-Sommerfeld conditions for 1D Toeplitz operators: hyperbolic case
Spectral Theory
2016-01-20 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
In this article, we state the Bohr-Sommerfeld conditions around a singular value of hyperbolic type of the principal symbol of a self-adjoint semiclassical Toeplitz operator on a compact connected K\"{a}hler surface. These conditions allow the description of the spectrum of the operator in a fixed size neighbourhood of the singularity. We provide numerical computations for three examples, each associated to a different topology.
Cite
@article{arxiv.1309.5322,
title = {Singular Bohr-Sommerfeld conditions for 1D Toeplitz operators: hyperbolic case},
author = {Yohann Le Floch},
journal= {arXiv preprint arXiv:1309.5322},
year = {2016}
}