Mathematics Colloquium via Zoom

Exponential Riesz bases in finite abelian groups and tightness quantities

Dr. Azita Mayeli

City University of New York

Abstract

Motivated by the open problem of existing a subset of $\Bbb R^d$ which do not admit any exponential Riesz basis, we focus on exponential Riesz bases in finite abelian groups. We show that every subset of a finite abelian group has such a basis, therefore removing the interest in the existence question in this context. We then introduce tightness quantities for subsets to measure the conditioning of Riesz bases. As a result, we obtain a new weak evidence in the favor of the open problem in the Euclidean space by presenting a sequence of subsets of $\Bbb Z_m^d$ whose tightness quantities go to infinity as $m$ goes to $\infty$. This talk is based on a joint work with Sam Ferguson and Nat Sothanaphan.

Zoom Meeting ID: 999 1481 2830

Passcode upon request.

Free