Orthogonal Frames of Translates

Details Orthogonal Frames of Translates Orthogonal Frames of Translates

2003-10-10

arxiv.org/abs/math/0310161v1

Mathematics

Functional Analysis

20 pages

Scientific paper

Two Bessel sequences are orthogonal if the composition of the synthesis operator of one sequence with the analysis operator of the other sequence is the 0 operator. We characterize when two Bessel sequences are orthogonal when the Bessel sequences have the form of translates of a finite number of functions in $\ltwod$. The characterizations are applied to Bessel sequences which have an affine structure, and a quasi-affine structure. These also lead to characterizations of superframes. Moreover, we characterize perfect reconstruction, i.e. duality, of subspace frames for translation invariant (bandlimited) subspaces of $\ltwod$.

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