Finite Sampling in Multiple Generated U-Invariant Subspaces

The relevance in sampling theory of U -invariant subspaces of a Hilbert space H, where U denotes a unitary operator on H, is nowadays a recognized fact. Indeed, shift-invariant subspaces of L(R) become a particular example; periodic extensions of finite signals provide also a remarkable example. As a consequence, the availability of an abstract U -sampling theory becomes a useful tool to handle these problems. In this paper we derive a sampling theory for finite dimensional multiple generated U -invariant subspaces of a Hilbert space H. As the involved samples are identified as frame coefficients in a suitable euclidean space, the relevant mathematical technique is that of finite frame theory. Since finite frames are nothing but spanning sets of vectors, the used technique naturally meets matrix analysis.