Nonstandard Representations of Locally Compact Groups

In the note, it is proved that, under natural conditions, any infinite-dimensional unitary representation $T$ of a direct product of groups $G=K\times N$, where $K$ is a compact group and $N$ is a locally compact Abelian group, is imaged by a representation of the nonstandard analog $\widetilde G$ of the group $G$ in the group of nonstandard matrices of a fixed nonstandard size.