Shift Invariant Spaces and Shift Generated Dual Frames for Local Fields - Ahmadi, A.; Hemmat, A. Askari (Communications in Mathematics and Applications, 2012)
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 $H^\perp$.