Abstract :
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.
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