Entire functions and gap theorems

Monday, April 6, 2009 - 4:00pm to Thursday, April 9, 2009 - 6:00pm
Several classical problems of Analysis can be translated into a universal language based on Hilbert spaces of entire functions and kernels of Toeplitz operators. Problems that can be treated this way include completeness/minimality problems for systems of exponentials or special functions in $L^2$ and spectral problems for second order differential operators. This approach was used to solve some of such problems in our recent papers with Nikolai Makarov.In this talk I will show how the Toeplitz approach can be used to extend the so-called Beurling's Gap Theorem on the existence of gaps in the Fourier transform of a measure and to solve the Polya-Levinson problem on sampling sets for entire functions of exponential type zero.
Alexei Poltoratski
Texas A&M University
Event Location: 
Fine Hall 110