On Some Sampling-Related Frames inU-Invariant Spaces

H. R. Fernández-Morales, A. G. García, M. A. Hernández-Medina, M. J. Muñoz-Bouzo
2013 Abstract and Applied Analysis  
This paper is concerned with the characterization as frames of some sequences inU-invariant spaces of a separable Hilbert spaceℋwhereUdenotes an unitary operator defined onℋ; besides, the dual frames having the same form are also found. This general setting includes, in particular, shift-invariant or modulation-invariant subspaces inL2ℝ, 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
more » ... g so, we need the unitary operatorUto belong to a continuous group of unitary operators.
doi:10.1155/2013/761620 fatcat:uruk64bupbgflear4fntmfthe4