This paper is concerned with the characterization as frames of some sequences in -invariant spaces of a separable Hilbert space where denotes an unitary operator defined on ; besides, the dual frames having the same form are also found. This general setting includes, in particular, shift-invariant or modulation-invariant subspaces in , 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 to belong to a continuous group of unitary operators.
"On Some Sampling-Related Frames in -Invariant Spaces." Abstr. Appl. Anal. 2013 1 - 14, 2013. https://doi.org/10.1155/2013/761620