Codes and Expansions (CodEx) Seminar

Shahaf Nitzan (Georgia Tech)
A few remarks on 'good' exponential Riesz bases

We say that a family of sets admits "good" exponential Riesz bases, if every set in the family admits an exponential Riesz basis, and the lower and upper bounds of these bases are universal throughout the family (up to appropriate normalizations). The similar notion of "good" exponential frames has been studied thoroughly in recent years. In particular, it has been shown that "good" exponential frames exist for the family of measurable subsets of the line, the torus, and the finite groups \(\mathbb{Z}/N\mathbb{Z}\). In this talk we will see that in contrast, some of these families do not admit 'good' exponential Riesz bases. Some open problems in this area will be discussed as well.

This talk is based on conversations with Gady Kozma and Alexander Olevskii.