Abstract
Motivated by the ordinary Gabor frames in L2(ℝd) and operator-valued frames on abstract Hilbert spaces, we investigate operator-valued Gabor frames associated with locally compact Abelian groups. Necessary and sufficient conditions for an operator-valued Gabor frame to admit a Parseval/tight Gabor dual are given. In particular, we consider a special case, which includes the case of ordinary Gabor frames.
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