Analysis Seminar

Stefan SteinerbergerYale University
Three miracles in analysis

Monday, November 14, 2016 - 2:30pm
Malott 406

I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that relies heavily on number theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is $\sin(x)$. (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in $L^2$ -- but this time from below (this problem originally arose in medical imaging). Here, the miracle being exploited is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).