On the self-similarity problem for Gaussian-Kronecker flows

Source abstract

It is shown that a countable symmetric multiplicative subgroup G = − H ∪ H G=-H\cup H with H ⊂ R + ∗ H\subset \mathbb {R}_+^\ast is the group of self-similarities of a Gaussian-Kronecker flow if and only if H H is additively Q \mathbb {Q} -independent. In particular, a real number s ≠ ± 1 s\neq \pm 1 is a scale of self-similarity of a Gaussian-Kronecker flow if and only if s s is transcendental. We also show that each countable symmetric subgroup of R ∗ \mathbb {R}^\ast can be realized as the group of self-similarities of a simple spectrum Gaussian flow having the Foiaş-Stratila property.