scholarly journals Dual frames in L2(0,1) connected with generalized sampling in shift-invariant spaces

2006 ◽  
Vol 20 (3) ◽  
pp. 422-433 ◽  
Author(s):  
A.G. García ◽  
G. Pérez-Villalón
Keyword(s):  
Dual Frames ◽  
Generalized Sampling ◽  
Shift Invariant Spaces ◽  
Invariant Spaces

scholarly journals On Some Sampling-Related Frames inU-Invariant Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
H. R. Fernández-Morales ◽  
A. G. García ◽  
M. A. Hernández-Medina ◽  
M. J. Muñoz-Bouzo
Keyword(s):  
Unitary Operator ◽  
Separable Hilbert Space ◽  
General Setting ◽  
Continuous Group ◽  
Unitary Operators ◽  
Dual Frames ◽  
Generalized Sampling ◽  
Sampling Problem ◽  
Perturbation Problems ◽  
Invariant Spaces

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 unitary operatorUto belong to a continuous group of unitary operators.

scholarly journals Generalized sampling in shift-invariant spaces with multiple stable generators

2008 ◽  
Vol 337 (1) ◽  
pp. 69-84 ◽  
Author(s):  
A.G. García ◽  
M.A. Hernández-Medina ◽  
G. Pérez-Villalón
Keyword(s):  
Generalized Sampling ◽  
Shift Invariant Spaces ◽  
Invariant Spaces
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