Nonuniform sampling in principal shift-invariant subspaces of mixed Lebesgue spaces Lp,q(Rd+1)

In this paper, we study the nonuniform sampling and reconstruction problem in shift-invariant subspaces of mixed Lebesgue spaces. We first show that shift invariant subspaces in mixed Lebesgue spaces L-p,L-q (Rd+1) can be well-defined. Then we propose that the sampling problem in shift-invariant subspaces of mixed Lebesgue spaces is well-posed. At last, the nonuniform samples {f(x(j), y(k)) : k, j is an element of J} of a function f belonging to a shift-invariant subspace of mixed Lebesgue spaces are proposed, and we give a fast reconstruction algorithm that allows exact reconstruction off as long as the sampling set X = {(x(j), y(k)) : k, j is an element of J} is sufficiently dense. (C) 2017 Elsevier Inc. All rights reserved.