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Random average sampling over quasi shift-invariant spaces on LCA groups

Ankush Kumar Garg, S. Arati, P. Devaraj

Abstract

The problem of random average sampling and reconstruction over multiply generated local quasi shift-invariant subspaces of mixed Lebesgue spaces in the setting of locally compact abelian groups is considered. The sampling inequalities as well as the reconstruction formulae are shown to hold with very high probability if the number of samples is taken to be sufficiently large.

Random average sampling over quasi shift-invariant spaces on LCA groups

Abstract

The problem of random average sampling and reconstruction over multiply generated local quasi shift-invariant subspaces of mixed Lebesgue spaces in the setting of locally compact abelian groups is considered. The sampling inequalities as well as the reconstruction formulae are shown to hold with very high probability if the number of samples is taken to be sufficiently large.
Paper Structure (4 sections, 10 theorems, 109 equations)

This paper contains 4 sections, 10 theorems, 109 equations.

Table of Contents

  1. Introduction
  2. A local quasi shift-invariant space
  3. Sampling inequalities
  4. Reconstruction formulae

Key Result

Lemma 2.1

For any $f \in V_{K}^{*}(\Phi), \|f\|_{L^{\infty}(\widetilde{K})} \leq \dfrac{\widetilde{C}_{\Phi}}{a_{1}},$ where and $a_{1}$ is as in assumption $(\text{A}_{2}).$

Theorems & Definitions (21)

  • Lemma 2.1
  • proof
  • Remark 2.2
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • proof
  • Lemma 2.6
  • ...and 11 more