On Some Sampling-Related Frames in -Invariant Spaces

H. R. Fernández-Morales, A. G. García, M. A. Hernández-Medina and M. J. Muñoz-Bouzo

Abstract and Applied Analysis, 2013, vol. 2013, 1-14

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:761620

DOI: 10.1155/2013/761620

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