Seminario di Analisi: On extremizers for Fourier restriction inequalities (Diogo Oliveira e Silva)

speaker: Diogo Oliveira e Silva (Hausdorff Center for mathematics - Bonn)

title: "On extremizers for Fourier restriction inequalities"

abstract:

This talk will focus on extremizers for a family of Fourier restriction inequalities on planar curves. It turns out that, depending on whether or not a certain geometric condition related to the curvature is satisfied, extremizing sequences of nonnegative functions may or may not have a subsequence which converges to an extremizer. We hope to describe the method of proof, which is of concentration compactness flavor, in some detail. Tools include bilinear estimates, a variational calculation, a modification of the usual method of stationary phase and several explicit computations.