Dynamics Seminar

Event Information Gap and Type Problems in Fourier Analysis
15:10 on Monday April 27, 2015
16:00 on Monday April 27, 2015
BA6183, Bahen Center, 40 St. George St.
Alexei Poltoratski

Texas A&M University

One of the basic problems of Harmonic analysis is to determine if a given collection of functions is complete in 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, posted 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.