The study of the existence of Riesz bases of exponentials has attracted considerable attention and it is still a very active research area. The main motivation behind this study is that the frequency set of such bases provides complete interpolating sequences for Paley-Wiener spaces. One important line of research considers the spectrum sets with the property of multi-tiling the space along translations of a lattice. It has been proved –by multiple authors, and with different approaches– that such sets admit a Riesz basis of exponentials whose frequency set is a finite union of translations of another lattice (the dual). The multi-tiling level determines the number of translations. However, these proofs only establish the existence of such bases and do not provide explicit stability bounds.

In this talk, we present a probabilistic approach to the problem. In particular, we show that taking O(k log k) random samples within [-1/2,1/2]^d and its periodizations is sufficient to construct a sampling set for the Paley-Wiener space of a union of k integer translations of the unitary cube with high probability, providingexplicit stability bounds. We obtain this result as a corollary of a random periodic sampling theorem for shift-invariant spaces generated by localized atoms with essentially disjoint frequency support.The talk is based on ongoing work in collaboration with Jorge Antezana and José Luis Romero.

https://univienna.zoom.us/j/62077153839?pwd=T3pxeHNRNEU0RlFoY1J2cnIzbzU5dz09