TY - JOUR
T1 - Finding duality for Riesz bases of exponentials on multi-tiles
AU - Frederick, Christina
AU - Okoudjou, Kasso A.
N1 - Funding Information:
The authors are grateful for discussions with David Walnut, Karamatou Yacoubou Djima, and Azita Mayeli. The authors also thank the anonymous reviewers for their helpful comments. The work of C. Frederick is partially supported by The National Science Foundation grant DMS-1720306 . K. A. Okoudjou was partially supported by The National Science Foundation under Grant No. DMS-1814253 , and an MLK visiting professorship at MIT .
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2021/3
Y1 - 2021/3
N2 - 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.
AB - 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.
KW - Biorthogonal systems
KW - Frames of exponentials
KW - Multi-tiling
KW - Riesz bases of exponentials
KW - Vandermonde systems
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U2 - 10.1016/j.acha.2020.10.006
DO - 10.1016/j.acha.2020.10.006
M3 - Article
AN - SCOPUS:85096208860
SN - 1063-5203
VL - 51
SP - 104
EP - 117
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
ER -