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

@article{Antezana2021SplittingTR,
title={Splitting the Riesz basis condition for systems of dilated functions through Dirichlet series},
author={Jorge Antezana and Daniel Carando and Melisa Scotti},
journal={Journal of Mathematical Analysis and Applications},
year={2021}
}
• Published 14 October 2021
• Mathematics
• Journal of Mathematical Analysis and Applications
Inspired by the work of Hedenmalm, Lindqvist and Seip, we consider different properties of dilations systems of a fixed function φ ∈ L(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 Dirichtet series and, also, in terms of Hardy spaces on the infinite polytorus. We also address the multivariate case.

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