$L^p$ norms of higher rank eigenfunctions and bounds for spherical functions
Analysis of PDEs
2016-06-22 v4 Number Theory
Representation Theory
Abstract
We prove almost sharp upper bounds for the norms of eigenfunctions of the full ring of invariant differential operators on a compact locally symmetric space, as well as their restrictions to maximal flat subspaces. Our proof combines techniques from semiclassical analysis with harmonic theory on reductive groups, and makes use of new asymptotic bounds for spherical functions that are of independent interest.
Keywords
Cite
@article{arxiv.1106.0534,
title = {$L^p$ norms of higher rank eigenfunctions and bounds for spherical functions},
author = {Simon Marshall},
journal= {arXiv preprint arXiv:1106.0534},
year = {2016}
}
Comments
57 pages, 1 figure. Substantially revised, and close to the published version