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On Some Sampling-Related Frames in -Invariant Spaces

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

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.

Suggested Citation

  • H. R. Fernández-Morales & A. G. García & M. A. Hernández-Medina & M. J. Muñoz-Bouzo, 2013. "On Some Sampling-Related Frames in -Invariant Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-14, November.
    • Handle: RePEc:hin:jnlaaa:761620
    DOI: 10.1155/2013/761620
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