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We prove the existence of Riesz bases of exponentials of L^2(Omega), providedthat Omega in R^d 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. We alsoextend known results for submulti-tiles and frames of exponentials to theunbounded case.

Riesz Bases of Exponentials on Unbounded Multi-tiles