Extension of shift-invariant frames for locally compact abelian groups

Authors

  • Mehdi Rashidi
  • Akbar Nazari

DOI:

https://doi.org/10.30495/jme.v8i0.254

Keywords:

Frames, locally compact abelian group, shift invariant space, dual frame.

Abstract

Let G be a locally compact abelian group with a uniform lattice sub-
group. In this paper, we verify extension of shift-invariant systems in L2(G) to tight frames. We show that any shift-invariant Bessel sequence with an at most countable number of generators in L2(G) can be extended to a tight frame for its closed linear span by adding another shift-invariant system with at most the same number of generators in L2(G). Also, we yield an extension of the given Bessel sequence to a pair of dual frame sequences.

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Published

2014-10-22

Issue

Vol. 8

Section

Vol. 8, No. 3, (2014)

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