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arXiv · 1910.09257

Finding duality for Riesz bases of exponentials on multi-tiles

Christina Frederick·Kasso Okoudjou
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Abstract

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

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Christina Frederick, Kasso Okoudjou. 2019-10-21. Finding duality for Riesz bases of exponentials on multi-tiles. https://arxiv.org/abs/1910.09257

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