Phase retrieval for continuous Gabor frames on locally compact abelian groups

In this paper, we study continuous frames from projective representations of locally compact abelian groups type $$\widehat{G}\times G$$ . particular, using the Fourier transform on groups, obtain a characterization maximal spanning vectors. As an application, for G, compactly generated Euclidean group or local field with odd residue characteristic, prove existence vectors, hence phase retrievability, associated $$(\widehat{G}\times G)$$ -frames.