FRAMES GENERATED BY ACTIONS OF COUNTABLE DISCRETE GROUPS

被引：0

作者：

Roysland, Kjetil ^{[1
]}

机构：

[1] Univ Oslo, Dept Math, NO-0316 Oslo, Norway

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 363卷 / 01期

关键词：

Frames; shift-invariant subspaces; multiresolution analysis and unitary group representations; PROJECTIVE MULTIRESOLUTION ANALYSES; MODULES; BASES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 subspace in L-2(R-n) 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.

引用

页码：94 / 107

页数：14

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