3. Harmonic Analysis Seminar.
Speaker: Iswarya Sitiraju (Louisiana State University)
Title: ANALYTIC WAVEFRONT SETS OF SPHERICAL
DISTRIBUTIONS ON THE DE SITTER SPACE
Time, Day and Date: 10:30 a.m., Wednesday, September 4
Venue: Online (Zoom): https://meet.google.com/kmo-osxt-zqh
Abstract: In this work, we determine the wavefront set of certain eigendistributions of the Laplace-Beltrami operator on the de Sitter space. Let G' = {O}_{1,n}(R) be the Lorentz group, and let H' = {O}_{1,n-1}(R) ' be its subset. The de Sitter space dS^n is a one-sheeted hyperboloid in R^{1+n} isomorphic to G'/H'. A {\it spherical distribution} is an H'-invariant eigendistribution of the Laplace-Beltrami operator on dS^n. The space of spherical distributions on the de Sitter space with eigenvalue \lambda, denoted by {D}'_{\lambda}, has dimension 2. We construct a basis for the space of positive-definite spherical distributions as boundary values of sesquiholomorphic kernels on the crown domains, which are open complex domains in dS^n_{C} containing dS^n on the boundary.
We then characterize the analytic wavefront set for such distributions.