https://www.math.northwestern.edu/people/faculty/steve-zelditch.html
Thu, January 27, 2022, 9:00-10:00 am PST via Zoom
Title: Spatial and Fourier restriction problems for eigenfunctions.
Abstract: There are two different types of “restriction theorems” for Laplace (or related) operators. One type is “Fourier restriction theorems” where the Fourier transform is restricted to a hypersurface or submanifold. Another type is spatial restriction theorems, where an eigenfunction $\phi$ of the Laplacian $\Delta_M$ of a Riemannian manifold is restricted to a submanifold $H$. My talk is about joint restriction theorems: one first restricts an eigenfunction $\phi$ to a submanifold $H$, expands it in eigenfunctions $e_k$ of $\Delta_H$, and then studies the Fourier restriction of $\phi |_H$ to short window of Fourier coefficients w.r.t. $H$. How much of the $L^2$-mass of $\phi |_H$ lies in a short window of frequencies of $H$? This kind of problem arises in several branches of analysis. My talk is in part a survey of joint restriction phenomena and in part a description of recent results, partly in collaboration with Yakun Xi and Emmett Wyman.