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arXiv · 1201.5733

On the self-similarity problem for Gaussian-Kronecker flows

Krzysztof Fraczek·Joanna Kulaga·Mariusz Lemanczyk
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Abstract

It is shown that a countable symmetric multiplicative subgroup $G=-H\cup H$ with $H\subset\mathbb{R}_+^\ast$ is the group of self-similarities of a Gaussian-Kronecker flow if and only if $H$ is additively $\mathbb{Q}$-independent. In particular, a real number $s\neq\pm1$ is a scale of self-similarity of a Gaussian-Kronecker flow if and only if $s$ is transcendental. We also show that each countable symmetric subgroup of $\mathbb{R}^\ast$ can be realized as the group of self-similarities of a simple spectrum Gaussian flow having the Foias-Stratila property.

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Krzysztof Fraczek, Joanna Kulaga, Mariusz Lemanczyk. 2012-05-21. On the self-similarity problem for Gaussian-Kronecker flows. https://arxiv.org/abs/1201.5733

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