Spectral estimates on the sphere
Analysis of PDEs
2016-01-20 v2
Abstract
In this article we establish optimal estimates for the first eigenvalue of Schr\"odinger operators on the d-dimensional unit sphere. These estimates depend on Lebsgue's norms of the potential, or of its inverse, and are equivalent to interpolation inequalities on the sphere. We also characterize a semi-classical asymptotic regime and discuss how our estimates on the sphere differ from those on the Euclidean space.
Cite
@article{arxiv.1301.1210,
title = {Spectral estimates on the sphere},
author = {Jean Dolbeault and Maria J. Esteban and Ari Laptev},
journal= {arXiv preprint arXiv:1301.1210},
year = {2016}
}