Spectral estimate for the Laplace-Beltrami operator on the hyperbolic half-plane
Abstract
The purpose of this note is to investigate the concentration properties of spectral projectors on manifolds. This question has been intensively studied (by Logvinenko--Sereda, Nazarov, Jerison--Lebeau, Kovrizhkin, Egidi--Seelmann--Veseli{\'c}, Burq--Moyano, among others) in connection with the uncertainty principle. We provide the first high-frequency results in a geometric setting which is neither Euclidean nor a perturbation of Euclidean. Namely, we prove the natural (and optimal) uncertainty principle for the spectral projector on the hyperbolic half-plane.
Keywords
Cite
@article{arxiv.2401.14977,
title = {Spectral estimate for the Laplace-Beltrami operator on the hyperbolic half-plane},
author = {Marc Rouveyrol},
journal= {arXiv preprint arXiv:2401.14977},
year = {2026}
}
Comments
17 pages. Comments are welcome. Published in Journal of Functional Analysis. Changes in v2 : abstract and Section 1.2 modified to reflect that this result is the first high-frequency spectral estimate on a non-Euclidean manifold, but not the first one altogether (see Rose and Tautenhahn : arXiv:2305.06916)