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^.