Special weak limits and simple spectrum of the tensor products of flows

An example of a measure-preserving flow $T_t$ for which the tensor product $T_t\otimes T_{\alpha t}$ has simple spectrum for all $\alpha > 1$ is constructed. The construction of the flow uses asymptotically infinitesimal spacers and spacers obtained using results in finite field theory. For the spectral measure $\sigma$ of a flow of this type, any nonorthogonal projection of the measure $\sigma\times\sigma$ onto the diagonal in $\mathbb R\times \mathbb R$ is a 1-1 mapping $(\operatorname{mod} 0)$ with respect to the measure $\sigma\times\sigma$.
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