Random sampling in multiply generated shift-invariant subspaces of mixed Lebesgue spaces Lp,q(R x Rd)

We mainly study the random sampling and reconstruction in multiply generated shift-invariant subspaces V-p,V-q(Phi) of mixed Lebesgue spaces L-p,L-q(R x R-d). Under suitable conditions for the generators Phi, we can prove that if the sampling sizes are large enough for both variables, the sampling stability holds with high probability for all functions in V-p,V-q(Phi) whose energy is concentrated on a compact subset. Finally, a reconstruction algorithm based on random samples is given for functions in a finite dimensional subspace. (C) 2020 Elsevier B.V. All rights reserved.