Riesz bases in L2(0, 1) related to sampling in shift-invariant spaces

The Fourier duality is an elegant technique to obtain sampling formulas in Paley–Wiener spaces. In this paper it is proved that there exists an analogue of the Fourier duality technique in the setting of shift-invariant spaces. In fact, any shift-invariant space Vϕ with a stable generator ϕ is the range space of a bounded one-to-one linear operator T between L2(0, 1) and L2(R). Thus, regular and irregular sampling formulas in Vϕ are obtained by transforming, via T , expansions in L2(0, 1) with respect to some appropriate Riesz bases.  2004 Elsevier Inc. All rights reserved.