Frames generated by actions of countable discrete groups
Functional Analysis
2009-11-24 v1
Abstract
We consider dual frames generated by actions of countable discrete groups on a Hilbert space. Module frames in a class of modules over a group algebra are shown to coincide with a class of ordinary frames in a representation of the group. This has applications to shift-invariant spaces and wavelet theory. One of the main findings in this paper is that whenever a shift-invariant sub space in L2(Rn) has compactly supported dual frame generators then it also has compactly supported bi-orthogonal generators. The crucial part in the proof is a theorem by Swan that states that every finitely generated projective module over the Laurent polynomials in n variables is free.
Keywords
Cite
@article{arxiv.0911.4210,
title = {Frames generated by actions of countable discrete groups},
author = {Kjetil Roysland},
journal= {arXiv preprint arXiv:0911.4210},
year = {2009}
}