On Some Sampling-Related Frames in U-Invariant Spaces

Abstract

This paper is concerned with the characterization as frames of some sequences in U-invariant spaces of a separable Hilbert space ℋ where U denotes an unitary operator defined on ℋ; besides, the dual frames having the same form are also found. This general setting includes, in particular, shift-invariant or modulation-invariant subspaces in L2ℝ, where these frames are intimately related to the generalized sampling problem. We also deal with some related perturbation problems. In doing so, we need the unitary operator U to belong to a continuous group of unitary operators.