Maximizers and near-maximizers for Fourier restriction inequalities

Abstract: Fourier restriction phenomena allow us to make sense out of the restriction of the Fourier transform of an $L^p$ function (nominally only defined almost everywhere) on measure zero sets, provided these sets possess sufficient curvature. In the dual formulation, "tubes" whose directions are restricted to lie along some curved set can only overlap with one another on a relatively small region of space. More quantitatively, such phenomena are reflected by Lebesgue space bounds for the Fourier restriction operator. In this talk, we will describe some open questions and recent results regarding the existence of functions that provide a worst-case scenario by saturating these Lebesgue space bounds.

Mathematics

Audience: researchers in the discipline

K-State Mathematics Department Women Lecture Series