Gabor duals for operator-valued Gabor frames on locally compact abelian groups (Q2173207)

In this paper, the authors studied an operator valued Gabor frame (OPV-Gabor frame) associated with locally compact abelian groups and proved two main results namely Theorem 3.1 and Theorem 3.2. Theorem 3.1 gives a necessary and sufficient condition for an OPV Gabor frame for \( L^2 (G)\) satisfying certain conditions to admit a Parseval OPV Gabor dual frame where Theorem 3.2 gives a necessary and sufficient condition for an operator valued Gabor frame for \( L^2 (G)\) to admit a tight OPV Gabor dual frame.