Nonuniform average sampling in multiply generated shift-invariant subspaces of mixed Lebesgue spaces

2018/06/12 by Qingyue Zhang, Zhang, Qingyue
Mathematics · #41A58 #42C15 #94A12 #94A20 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1806.05055

openalex publication_date 2018/06/12 · openalex created_date 2018/06/21 · openalex updated_date 2026/07/28

Abstract

In this paper, we study nonuniform average sampling problem in multiply generated shift-invariant subspaces of mixed Lebesgue spaces. We discuss two types of average sampled values: average sampled values \ ⟨ f,ψ_a(⋅-x_j,⋅-y_k) ⟩:j,k∈\mathbbJ\ generated by single averaging function and average sampled values \ ⟨ f,ψ_x_j,y_k ⟩:j,k∈\mathbbJ\ generated by multiple averaging functions. Two fast reconstruction algorithms for this two types of average sampled values are provided.

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