Finding duality and Riesz bases of exponentials on multi-tiles
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It is known that if Ω⊂R^d is bounded, measurable set that forms a k-tiling of R^d when translated by a lattice L, there exists a Riesz basis of exponentials for L^2(Ω) constructed using k translates of the dual lattice L^*. In this paper we give an explicit construction of the corresponding bi-orthogonal dual Riesz basis. In addition, we extend the iterative sampling algorithm introduced in prior work to this multivariate setting.
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