Aldroubi, Akram; Sun, Qiyu; Tang, Wai-Shing Non-uniform sampling in multiply generated shift-invariant subspaces of \(L^p(\mathbb{R}^d)\). (English) Zbl 1025.42025 Deng, Donggao (ed.) et al., Wavelet analysis and applications. Proceedings of an international conference, Guangzhou, China, November 15-20, 1999. Providence, RI: American Mathematical Society (AMS). AMS/IP Stud. Adv. Math. 25, 1-8 (2002). It is proposed a reconstruction algorithm with irregular sufficiently dense sampling for the shift invariant subspace \[ V^p (\Phi) = \bigl\{ f = \sum\limits_{k\in {\mathbb Z}^d} C^{T}(k) \Phi(x - k) : C\in (l^p)^r\bigr\} \subset L^p({\mathbb R}^d) \] with a given generator \(\Phi = (\Phi_1,\ldots,\Phi_r)^{T}\) satisfying certain additional conditions.For the entire collection see [Zbl 0983.00042]. Reviewer: Sergei V.Rogosin (Minsk) Cited in 5 Documents MSC: 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 65T60 Numerical methods for wavelets 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 41A27 Inverse theorems in approximation theory Keywords:irregular sampling; shift invariant spaces; reconstruction PDFBibTeX XMLCite \textit{A. Aldroubi} et al., AMS/IP Stud. Adv. Math. 25, 1--8 (2002; Zbl 1025.42025)