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

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局部紧致阿贝尔群上连续Gabor框架的相位检索

在本文中，我们从\（\ widehat {G} \ times G \）类型的局部紧致阿贝尔群的投影表示中研究连续帧。特别是，对局部紧致的阿贝尔群使用傅立叶变换，我们获得了最大跨度矢量的特征。作为一个应用，对于G（一个紧密生成的局部欧几里得局部紧的阿贝尔群或具有奇数残基特征的局部场），我们证明了相关\\（（\ widehat {G} \ times G）\）-帧。