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Generalized sampling: from shift-invariant to U-invariant spaces

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URI: https://hdl.handle.net/10016/36166
ISSN: 0219-5305
DOI: https://doi.org/10.1142/S0219530514500213
UXXI: AR/0000016837
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generalized_AA_2015_ps.pdf (301.65 KB)
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2015-05-01
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World Scientific Publishing
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The aim of this article is to derive a sampling theory in U-invariant subspaces of a separable Hilbert space ℋ where U denotes a unitary operator defined on ℋ. To this end, we use some special dual frames for L2(0, 1), and the fact that any U-invariant subspace with stable generator is the image of L2(0, 1) by means of a bounded invertible operator. The used mathematical technique mimics some previous sampling work for shift-invariant subspaces of L2(ℝ). Thus, sampling frame expansions in U-invariant spaces are obtained. In order to generalize convolution systems and deal with the time-jitter error in this new setting we consider a continuous group of unitary operators which includes the operator U.
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Stationary sequences, U-invariant subspaces, Frames, Dual frames, Time-jitter error, Group of unitary operators, Pseudo-dual frames
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Analysis and Applications, (2015), 13(3), pp. 303-329.
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