A time domain characterization of weak Gabor dual frames on the half real line

Abstract

Due to R+ not being a group under addition, L2 (R+) admits no traditional Gabor system as L2 (R). Observing that R+ is a group under a new addition “⊕”, we in this paper introduce and characterize a class of weak Gabor dual frames in L2 (R+) based on this new group structure. Some examples are also provided.