Exponential frames and syndetic Riesz sequences

Analysis Seminar
Wednesday, September 19, 2018 - 1:55pm
1 hour (actually 50 minutes)
Skiles 005
University of Oregon
In this talk we shall explore some of the consequences of the solution to the Kadison-Singer problem. In the first part of the talk we present results from a joint work with Itay Londner. We show that every subset $S$ of the torus of positive Lebesgue measure admits a Riesz sequence of exponentials $\{ e^{i\lambda x}\} _{\lambda \in \Lambda}$ in $L^2(S)$ such that $\Lambda\subset\mathbb{Z}$ is a set with gaps between consecutive elements bounded by $C/|S|$. In the second part of the talk we shall explore a higher rank extension of the main result of Marcus, Spielman, and Srivastava, which was used in the solution of the Kadison-Singer problem.