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| Title:
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Generalized shift-invariant systems and frames for subspaces |
| Type:
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Journal articleJournal article |
| Participant(s):
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Technical University of Denmark
Email:
Forfatter:
Eldar, Y.C.
Technical University of Denmark
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| Abstract:
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Let T-k denote translation by k is an element of Z(d). Given countable collections of functions {phi(j)}(j is an element of J), {(phi) over bar (j)}(j is an element of J) subset of L-2(R-d) and assuming that {T(k)phi(j)}(j is an element of J,k is an element of Z)(d) and {T-k(phi) over bar (j)} (d)(j is an element of J,k is an element of Z) are Bessel sequences, we are interested in expansions [GRAPHICS] Our main result gives an equivalent condition for this to hold in a more general setting than described here, where translation by k is an element of Z(d) is replaced by translation via the action of a matrix. As special cases of our result we find conditions for shift-invariant systems, Gabor systems, and wavelet systems to generate a subspace frame with a corresponding dual having the same structure. |
| Published:
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in journal: Journal of Fourier Analysis and Applications (ISSN: 1069-5869) (DOI: http://dx.doi.org/10.1007/s00041-005-4030-0), vol: 11, issue: 3, pages: 299-313, 2005 |
| DOI:
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