Generalized sampling in shift-invariant spaces with multiple stable generators

The aim of this paper is to derive stable generalized sampling in a shift-invariant space with stable generators. This is done in the light of the theory of frames in the product Hilbert space L2 (0, 1) := L2(0, 1) × ··· × L2(0, 1) ( times). The generalized samples are expressed as the frame coefficients of an appropriate function in L2 (0, 1) with respect to some particular frame in L2 (0, 1). Since any multiply stable generated shift-invariant space is the image of L2 (0, 1) by means of a bounded invertible operator, the generalized sampling is obtained from some dual frame expansions in L2 (0, 1). An example in the setting of the Hermite cubic splines is exhibited. © 2007 Elsevier Inc. All rights reserved