Analytic eigenbranches in the semi-classical limit
Spectral Theory
2022-09-08 v1 Analysis of PDEs
Abstract
We consider a one parameter family of Laplacians on a closed manifold and study the semi-classical limit of its analytically parametrized eigenvalues. Our results are analogous to a theorem for scalar Schr\"odinger operators on Euclidean space by Luc Hillairet and apply to geometric operators like Witten's Laplacian associated with a Morse function.
Cite
@article{arxiv.2001.07154,
title = {Analytic eigenbranches in the semi-classical limit},
author = {Stefan Haller},
journal= {arXiv preprint arXiv:2001.07154},
year = {2022}
}