BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Stefan Steinerberger (University of Washington) DTSTART:20211110T170000Z DTEND:20211110T180000Z DTSTAMP:20260423T052455Z UID:HAeS/21 DESCRIPTION:Title: Th e Smoothest Average and New Uncertainty Principles for the Fourier Transfo rm\nby Stefan Steinerberger (University of Washington) as part of Harm onic analysis e-seminars\n\n\nAbstract\nSuppose you are given a real-value d function f(x) and want to compute a local average at a certain scale. Wh at we usually do is to pick a nice probability measure u\, centered at 0 a nd having standard deviation at the desired scale\, and convolve. Classica l candidates for u are the characteristic function or the Gaussian. This g ot me interested in finding the ”best” function u – this problem com es in two parts: (1) describing what one considers to be desirable propert ies of the convolution and (2) understanding which functions satisfy these properties. I tried a basic notion for the first part\, ”the convolutio n should be as smooth as the scale allows”\, and ran into fun classical Fourier Analysis that seems to be new: (a) new uncertainty principles for the Fourier transform\, (b) that potentially have the characteristic funct ion as an extremizer\, (c) which leads to strange new patterns in hypergeo metric functions and (d) produces curious local stability inequalities. No ah Kravitz and I managed to solve two specific instances on the discrete l attice completely\, this results in some sharp weighted estimates for poly nomials on the unit interval – both the Dirichlet and the Fejer kernel m ake an appearance. The entire talk will be completely classical Harmonic A nalysis\, there are lots and lots of open problems.\n LOCATION:https://researchseminars.org/talk/HAeS/21/ END:VEVENT END:VCALENDAR