TIME-FREQUENCY LOCALIZATIONS FOR MODULATION SPACES ON LOCALLY COMPACT ABELIAN GROUPS

摘要

In the present paper we define weighted modulation spaces on a LCA group g with respect to a window function drawn from a suitable Banach space of test functions and prove a theorem to establish uncertainty principle for these modulation spaces. Also, using the concept of Zak transform, we generalize an earlier result of Heil (1990) on the Balian-Low theorem for the Wiener amalgam space W(C{sup}0,l{sup}1}(g). Our theorems include the corresponding results on Euclidean spaces as particular cases.