A constrained optimization problem for the Fourier transform

Analysis Seminar
Wednesday, February 7, 2018 - 1:55pm
1 hour (actually 50 minutes)
Skiles 005
UC Berkeley
Among functions $f$ majorized by indicator functions $1_E$, which functions have maximal ratio $\|\widehat{f}\|_q/|E|^{1/p}$? I will briefly describe how to establish the existence of such functions via a precompactness argument for maximizing sequences. Then for exponents $q\in(3,\infty)$ sufficiently close to even integers, we identify the maximizers and prove a quantitative stability theorem.