Colloquium: "Gap and Type Problems in Harmonic Analysis"

Alex Poltoratski, Texas A&M

Abstract: One of the basic problems of Harmonic analysis is to determine if a given collection of functions spans a given Hilbert space. A classical theorem by Beurling and Malliavin solved such a problem in the case when the space is $L^2$ on an interval and the collection consists of complex exponentials. Two closely related problems, the so-called Gap and Type Problems, formulated over 50 years ago, remained open until recently. In my talk I will present solutions to the Gap and Type problems and discuss their connections with adjacent fields of analysis.

Host: John McCarthy

Tea @ 3:45 in Cupples I, room 200