$L^p$ norms of higher rank eigenfunctions and bounds for spherical functions

Abstract

We prove almost sharp upper bounds for the $L^p$ 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.

57 pages, 1 figure. Substantially revised, and close to the published version

Cited by in corpus (5)

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• Schrödinger equations on compact globally symmetric spaces
• Bounds of restriction of characters to submanifolds
• $L^p$-Norm Bounds for Automorphic Forms via Spectral Reciprocity
• An estimate for spherical functions on $\mathrm{SL}(3,\mathbb{R})$