[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2012.49.3.571

SHIFT GENERATED DUAL FRAMES FOR LOCALLY COMPACT ABELIAN GROUPS

Ahmadi, Ahmad (Department of Mathematics Hormozgan University)
Askari-Hemmat, Ataollah (Department of Mathematics Kerman Graduate University of Technology, Department of Mathematics Shahid Bahonar University of Kerman)

Publication Information

Journal of the Korean Mathematical Society / v.49, no.3, 2012 , pp. 571-583 More about this Journal

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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