Simon L. Marshall
L^p bounds for eigenfunctions on locally symmetric spaces
Abstract: Abstract: There is a classical theorem of Sogge that provides bounds for the L^p norms of a Laplace eigenfunction on a compact Riemannian manifold, that are sharp on the sphere and for spectral clusters. I will present a generalization of this theorem to eigenfunctions of the full ring of invariant differential operators on a locally symmetric space, as well as a theorem on the restriction of eigenfunctions to maximal flat subspaces. Time permitting, I will discuss ways in which these bounds can be improved using inputs from number theory.
Friday December 6, 2013 at 3:00 PM in SEO 636