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

ANTEZANA, JORGE; CARANDO, DANIEL; SCOTTI, MELISA

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2022 vol. 507

0022-247X

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.