Finding duality for Riesz bases of exponentials on multi-tiles

Christina Frederick; Kasso A. Okoudjou

doi:10.1016/j.acha.2020.10.006

Finding duality for Riesz bases of exponentials on multi-tiles

Christina Frederick, Kasso A. Okoudjou

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

It is known [6,14,19] that if Ω⊂R^d 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.

Original language	English (US)
Pages (from-to)	104-117
Number of pages	14
Journal	Applied and Computational Harmonic Analysis
Volume	51
DOIs	https://doi.org/10.1016/j.acha.2020.10.006
State	Published - Mar 2021

All Science Journal Classification (ASJC) codes

Applied Mathematics

Keywords

Biorthogonal systems
Frames of exponentials
Multi-tiling
Riesz bases of exponentials
Vandermonde systems

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10.1016/j.acha.2020.10.006

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title = "Finding duality for Riesz bases of exponentials on multi-tiles",

abstract = "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.",

keywords = "Biorthogonal systems, Frames of exponentials, Multi-tiling, Riesz bases of exponentials, Vandermonde systems",

author = "Christina Frederick and Okoudjou, \{Kasso A.\}",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2021",

month = mar,

doi = "10.1016/j.acha.2020.10.006",

language = "English (US)",

volume = "51",

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T1 - Finding duality for Riesz bases of exponentials on multi-tiles

AU - Frederick, Christina

AU - Okoudjou, Kasso A.

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

UR - https://www.scopus.com/pages/publications/85096208860

UR - https://www.scopus.com/inward/citedby.url?scp=85096208860&partnerID=8YFLogxK

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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 -

Finding duality for Riesz bases of exponentials on multi-tiles

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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