Riesz bases of exponentials on unbounded multi-tiles

CABRELLI, CARLOS; CARBAJAL, DIANA

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

AMER MATHEMATICAL SOC

Año: 2018 vol. 146 p. 1991 - 2004

0002-9939

We prove the existence of Riesz bases of exponentials of L2(Ω),provided that Ω ⊂ Rd is a measurable set of finite and positive measure, notnecessarily bounded, that satisfies a multi-tiling condition and an arithmeticproperty that we call admissibility. This property is satisfied for any boundeddomain, so our results extend the known case of bounded multi-tiles. Wealso extend known results for submulti-tiles and frames of exponentials to theunbounded case.