%0 Journal Article
%T Frames generated by actions of countable discrete groups
%A Kjetil Roysland
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0911.4210v1