Bounds for spectral projectors on tori
Analysis of PDEs
2022-06-22 v4 Classical Analysis and ODEs
Number Theory
Abstract
We investigate norms of spectral projectors on thin spherical shells for the Laplacian on tori. This is closely related to the boundedness of resolvents of the Laplacian, and to the boundedness of norms of eigenfunctions of the Laplacian. We formulate a conjecture, and partially prove it.
Cite
@article{arxiv.2104.13274,
title = {Bounds for spectral projectors on tori},
author = {Pierre Germain and Simon Leo Rydin Myerson},
journal= {arXiv preprint arXiv:2104.13274},
year = {2022}
}
Comments
18 pages, statement of Theorem 1.2 simplified with resulting changes in Corollary 1.3