Equivalent Condition to a Frame Sequence
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Keywords:
Abelian Group, frame Sequence, Fourier transform, subgroupAbstract
Let G be a second countable locally compact abelian group and H a countable closed discrete subgroup of G such that the quotient group G/H is compact. A simple proof of characterization of frame generated by a function $\phi \in L^{2}(G)$ and its translates by elements of H in terms of the boundedness of the periodization of its Fourier transform $\hat{\phi }$ is given.
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