On zeros of lacunary polynomials and completeness of certain exponential families

17.03.2023 09:45 - 10.03.2023 11:15

Ilia Zlotnikov (University of Vienna)

Completeness and frame properties of the exponential systems in different function spaces are a classical subject of investigation.  

In particular, the systems of the form {t^k e^{2\pi i nt}: k=0,...,N, n\in\Z} are also well studied. We consider somewhat more general systems  E(S):={t^k e^{2\pi i nt}: t=0,...,N, k\in S, n\in\Z } where S is a fixed subset of non-negative integers.  

It turns out that both completeness and frame properties of E(S) depend on the structure of the set S, and may substantially differ from the case S={0,...,N}. This phenomenon is closely connected to certain properties of the zero sets of lacunary polynomials and generalized Vandermonde matrices. The talk is based on joint work with A. Kulikov and A. Ulanovskii



K. Gröchenig, J. L. Romero and I. Shafkulovska
SR11 (second floor)