Frame of translates and its canonical dual in L2(G)

Abstract

Let [Formula: see text] be a locally compact group. This work aims to study some important properties of the frame of translates for the space [Formula: see text]. Also, we showed that the frame of translates can be a frame for a proper subspace of [Formula: see text], in the case that [Formula: see text] has a contractive automorphism. Furthermore, we characterize the frame properties for such systems and find an expression for the canonical dual frame.