Finding duality for Riesz bases of exponentials on multi-tiles

Christina Frederick, Kasso A. Okoudjou

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)104-117
Number of pages14
JournalApplied and Computational Harmonic Analysis
Volume51
DOIs
StatePublished - 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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