Sampling-related frames in finite U-invariant subspaces

Recently, a sampling theory for infinite dimensional U  -invariant subspaces of a separable Hilbert space HH where U   denotes a unitary operator on HH has been obtained. Thus, uniform average sampling for shift-invariant subspaces of L2(R)L2(R) becomes a particular example. As in the general case it is possible to have finite dimensional U-invariant subspaces, the main aim of this paper is to derive a sampling theory for finite dimensional U  -invariant subspaces of a separable Hilbert space HH. Since the used samples are frame coefficients in a suitable euclidean space CNCN, the problem reduces to obtain dual frames with a U-invariance property.