Approximately dual and perturbation results for generalized translation-invariant frames on LCA groups

摘要

The results in this paper can be divided into three parts. First, we generalize the recent results of Benavente, Christensen and Zakowicz on approximately dual generalized shift-invariant frames on the real line to generalized translation-invariant (GTI) systems on locally compact abelian (LCA) groups. Second, we explain in detail how GTI frames can be realized as g-frames. Finally, the known results on perturbation of g-frames and results on perturbation of generalized shift-invariant systems are applied and extended to GTI systems on LCA groups.