Finding duality for Riesz bases of exponentials on multi-tiles

It is known [6,14,19] that if Ω⊂Rd belongs to a class of k-tiling domains when translated by a lattice Λ, there exists a Riesz basis of exponentials for L2(Ω) constructed using k translates of the dual lattice Λ⁎. In this paper, we give an explicit construction of the corresponding biorthogonal dual...

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Bibliographic Details
Published inApplied and computational harmonic analysis Vol. 51; pp. 104 - 117
Main Authors Frederick, Christina, Okoudjou, Kasso A.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2021
Subjects
Biorthogonal systems
Frames of exponentials
Multi-tiling
Riesz bases of exponentials
Vandermonde systems
Biorthogonal systems
Frames of exponentials
Riesz bases of exponentials
Multi-tiling
Vandermonde systems
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Summary:It is known [6,14,19] that if Ω⊂Rd belongs to a class of k-tiling domains when translated by a lattice Λ, there exists a Riesz basis of exponentials for L2(Ω) constructed using k translates of the dual lattice Λ⁎. In this paper, we give an explicit construction of the corresponding biorthogonal dual Riesz basis. We also extend the iterative reconstruction algorithm introduced in [11] to this setting.
ISSN:1063-5203
1096-603X
DOI:10.1016/j.acha.2020.10.006