Frames of translates by semiregular sampling

Authors

  • Hamidreza Rahimi Central Tehran Branch, Is- lamic Azad University, Tehran, Iran.
  • F Valizadeh Central Tehran Branch, Islamic Azad University, Tehran, Iran
  • R. A. Kamyabi Gol Ferdowsi University of Mashhad, and Center of Excellence in Analysis on Algebraic Structures (CEAAS)
  • F. Esmaeelzadeh Bojnourd Branch, Islamic Azad University, Bojnourd, Iran

Keywords:

frames, Riesz bases, semi-irregular translates, sampling

Abstract

In this paper, we consider some kinds of semiregular frames  of translates on the Hilbert space $L^2(\mathbb{R}^d)$. More precisely,  we investigate the frames of the form $\{T_{\mathcal{A}k}f\}_{k\in \mathbb{Z}^d}$, where $\mathcal{A}$ is a real  invertible  $d\times d$ matrix and $f\in L^2(\mathbb{R}^d)$,  and it is a frame for the  closed subspace generated by $\{T_{\mathcal{A}k}f\}_{k\in \mathbb{Z}^d}$.

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Published

2022-03-14

Issue

Vol. 16

Section

Vol. 16, No. 11, (2022)

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