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SHIFT GENERATED DUAL FRAMES FOR LOCALLY COMPACT ABELIAN GROUPS

  • Ahmadi, Ahmad ;
  • Askari-Hemmat, Ataollah
  • Received : 2010.07.08
  • Published : 2012.05.01

Abstract

Let $G$ be a metrizable, ${\sigma}$-compact locally compact abelian group with a compact open subgroup. In this paper we define the Gramian and the dual Gramian operators for shift invariant subspaces of $L^2(G)$ and we use them to characterize shift generated dual frames for shift in- variant spaces, which forms a frame for a subspace of $L^2(G)$. We present necessary and sufficient conditions for which standard dual is a unique SG-dual frame of type I and type II.

Keywords

frames;Gramian operator;locally compact abelian group;shift invariant space;SG-dual frame

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