Shift Invariant Spaces and Shift Generated Dual Frames for Local Fields

A. Ahmadi, A. Askari Hemmat

Abstract


Let $G$ be a locally compact Abelian group with a compact open subgroup $H$ and $X$ be a shift invariant subspace of $L^2(G)$ which forms a frame for a closed subspace of $L^2(G)$, then the dual frame of $X$ which is a shift invariant space, is called shift generated dual frame. In the present paper, we first define shift generated dual frame of type I and type II for a locally compact Abelian group with a compact open subgroup. Next, we present a characterization of shift generated dual frame in terms of fibers $H^\perp$.

Keywords


Dual frames; Locally compact Abelian group; Shift invariant space; SG-dual frame

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v3i3.205

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