Abstract
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 V φ with a stable generator φ is the range space of a bounded one-to-one linear operator T between L 2 ( 0 , 1 ) and L 2 ( R ) . Thus, regular and irregular sampling formulas in V φ are obtained by transforming, via T, expansions in L 2 ( 0 , 1 ) with respect to some appropriate Riesz bases.
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