Generalized sampling in shift invariant spaces with frames

Generalized sampling in a shift invariant subspace V of L2 (R) is considered. A function f in V is processed with different filters Lm and then one tries to reconstruct f from the samples Lmf (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?