Generalized sampling in shift invariant spaces with frames

Generalized sampling in a shift invariant subspace V of L 2(.) is considered. A function f in V is processed with different filters L m and then one tries to reconstruct f from the samples L m f(j.k). We develop a theory of how to do this in the case when V possesses a shift invariant frame. Special attention is paid to the question: How to obtain dual frames with compact support?