Remarks on Frames from Projective Representations of Locally Compact Groups

A projective representation of a locally compact group does phase retrieval if it admits a maximal spanning frame vector. In this paper, we provide a characterization of maximal spanning vectors for type I and square integrable irreducible projective representations of separable locally compact abelian groups. This generalizes the well-known criterion for the time–frequency case and unifies previous criteria for finite groups case and locally compact Gabor case. As an application, we show that irreducible projective representations of compact abelian groups do phase retrieval.