A RANGE FUNCTION APPROACH TO SHIFT-INVARIANT SPACES ON LOCALLY COMPACT ABELIAN GROUPS

摘要

This paper develops several aspects of shift-invariant spaces on locally compact abelian groups. For a second countable locally compact abelian group G we prove a useful Hilbert space isomorphism, introduce range functions and give a characterization of shift-invariant subspaces of L2(G) in terms of range functions. Utilizing these functions, we generalize characterizations of frames and Riesz bases generated by shifts of a countable set of generators from L2(ℝn) to L2(G).