Splitting the Riesz basis condition for systems of dilated functions through Dirichlet series

Inspired by the work of Hedenmalm, Lindqvist and Seip, we consider different properties of dilations systems of a fixed function φ∈L2(0,1). More precisely, we study when the system {φ(nx)}n is a Bessel sequence, a Riesz sequence, or it satisfies the lower frame bound. We are able to characterize these properties in terms of multipliers of the Hardy space H2 of Dirichlet series and, also, in terms of Hardy spaces on the infinite polytorus. We also address the multivariate case.