Friday November 20, 2009
4:00 - 5:00 pm
Milner Hall 317
4:00 - 5:00 pm
Milner Hall 317
Alex Poltoratski, Texas A&M University
Entire functions and gap theorems
In my talk I will discuss solutions to two problems of classical analysis obtained using an approach recently developed in our joint papers with Nikolai Makarov. A sequence of real numbers is called a Polya sequence if any entire function of exponential type zero that is bounded on that sequence is a constant. The first problem that I will discuss is an old problem by Polya and Levinson that asks for a description of such sequences. This part is based on joint work with my student Mishko Mitkovski. The second problem is the Beurling's gap problem. If X is a closed set on the real line, denote by GX the supremum of the size of the gap in the support of the Fourier transform of μ, taken over all non-trivial complex measures μ supported on X. I will present a formula for GX in terms of metric characteristics of X.
Entire functions and gap theorems
In my talk I will discuss solutions to two problems of classical analysis obtained using an approach recently developed in our joint papers with Nikolai Makarov. A sequence of real numbers is called a Polya sequence if any entire function of exponential type zero that is bounded on that sequence is a constant. The first problem that I will discuss is an old problem by Polya and Levinson that asks for a description of such sequences. This part is based on joint work with my student Mishko Mitkovski. The second problem is the Beurling's gap problem. If X is a closed set on the real line, denote by GX the supremum of the size of the gap in the support of the Fourier transform of μ, taken over all non-trivial complex measures μ supported on X. I will present a formula for GX in terms of metric characteristics of X.