Gabor Duals for Operator-valued Gabor Frames on Locally Compact Abelian Groups

摘要

Motivated by the ordinary Gabor frames in L-2(Double-struck capital R-d) 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.