Shift Invariant Spaces and Shift Generated Dual Frames for Local Fields

Authors

  • A. Ahmadi Department of Mathematics, Hormozgan University, Bandar Abbas
  • A. Askari Hemmat Department of Mathematics,Shahid Bahonar University of Kerman; Department of Mathematics, Kerman Graduate University of technology, Kerman; International Center for science High Technology and Environment Science, Kerman

DOI:

https://doi.org/10.26713/cma.v3i3.205

Keywords:

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

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 $H^\perp$.

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References

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CITATION

How to Cite

Ahmadi, A., & Hemmat, A. A. (2012). Shift Invariant Spaces and Shift Generated Dual Frames for Local Fields. Communications in Mathematics and Applications, 3(3), 205–214. https://doi.org/10.26713/cma.v3i3.205

Issue

Vol. 3 No. 3 (2012)

Section

Research Article

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