Journal article
Generalized shift-invariant systems and frames for subspaces
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.
Language: | English |
---|---|
Publisher: | Birkhäuser-Verlag |
Year: | 2005 |
Pages: | 299-313 |
ISSN: | 15315851 and 10695869 |
Types: | Journal article |
DOI: | 10.1007/s00041-005-4030-0 |
ORCIDs: | Christensen, Ole |