An optimal result for sampling density in shift-invariant spaces generated by Meyer scaling function

Fora class of continuously differentiable function phi satisfying certain decay conditions, it is shown that if the maximum gap delta := sup(x(i+1) - xi) between the consecutive sample points is smaller than a certain number B-0, then any f is an element of V(phi) can be reconstructed uniquely and stably. As a consequence of this result, it is shown that if delta < 1, then {xi : i is an element of Z} is a stable set of sampling for V(phi) with respect to the weight {w(i) : i is an element of Z}, where w(i) = (x(i+1) - x(i-1))/2 and phi is the scaling function associated with Meyer wavelet. Further, the maximum gap condition S <1 is sharp. (C) 2017 Elsevier Inc. All rights reserved.