Extension of Shift-Invariant Frames for Locally Compact Abelian Groups

Let g be a locally compact abelian group with a uniformlattice subgroup. in this paper, we verify extension of shift-invariantsystems in l2(g) to tight frames. we show that any shift-invariantbessel sequence with an at most countable number of generators inl2(g) can be extended to a tight frame for its closed linear span byadding another shift-invariant system with at most the same numberof generators in l2(g). also, we yield an extension of the given besselsequence to a pair of dual frame sequences.