Spectral gaps and completeness of complex exponentials

School of Mathematics Colloquium
Thursday, November 3, 2011 - 11:05pm for 1 hour (actually 50 minutes)
Skiles 006
Alexei Poltoratski – Texas A&M
Michael Lacey
One of the basic problems of Harmonic analysis is to determine ifa given collection of functions is complete in a given Hilbert space. Aclassical theorem by Beurling and Malliavin solved such a problem in thecase when the space is $L^2$ on an interval and the collection consists ofcomplex exponentials. Two closely related problems, the so-called Gap andType Problems, studied by Beurling, Krein, Kolmogorov, Levinson, Wiener andmany others, remained open until recently.In my talk I will  present solutions to the Gap and Type problems anddiscuss their connectionswith adjacent fields.