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

Details L^p bounds for higher rank eigenfunctions and asymptotics of spherical functions L^p bounds for higher rank eigenfunctions and asymptotics of spherical functions

2011-06-02

arxiv.org/abs/1106.0534v1

Mathematics

Analysis of PDEs

44 pages, 1 figure

Scientific paper

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. Our proof combines techniques from semiclassical analysis with harmonic theory on reductive groups, and makes use of asymptotic bounds for spherical functions which improve upon those of Duistermaat, Kolk and Varadarajan and are of independent interest.

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