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It is known that if $\Omega \subset \mathbb{R}^{d}$ belongs to a class ofmulti-tiling domains when translated by a lattice $\Lambda$, there exists aRiesz basis of exponentials for $L^{2}(\Omega)$ constructed using $k$translates of the dual lattice $\Lambda^*$. In this paper, we give an explicitconstruction of the corresponding biorthogonal dual Riesz basis. We also extendthe iterative reconstruction algorithm introduced in prior work to thissetting.

Finding duality for Riesz bases of exponentials on multi-tiles