Spectral cluster bounds for orthonormal functions (Dr. Julien Sabin, Université Paris-Sud)

Abstract: Sogge's L^p bounds are a way to measure the concentration of eigenfunctions of the Laplace-Beltrami operator on compact Riemannian manifolds associated to large eigenvalues. We generalize these bounds to systems of orthonormal functions, building a bridge between Sogge's result about concentration and the Weyl law, which in some sense is a manifestation of non-concentration. The optimality of these new bounds is also discussed. These spectral cluster bounds follow from Schatten-type bounds on oscillatory integral operators.

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Mar 02, 2017
from 02:00 PM to 03:00 PM


MAB 119

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