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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].

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
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