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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

On the self-similarity problem for Gaussian-Kronecker flows


Authors: Krzysztof Fraczek, Joanna Kułaga and Mariusz Lemańczyk
Journal: Proc. Amer. Math. Soc. 141 (2013), 4275-4291
MSC (2010): Primary 37A10, 60G15; Secondary 43A05, 43A46, 37A50, 37A45
Published electronically: August 8, 2013
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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 \pm 1$ 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 Foiaş-Stratila property.


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Additional Information

Krzysztof Fraczek
Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland
Email: fraczek@mat.umk.pl

Joanna Kułaga
Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland
Email: joanna.kulaga@gmail.com

Mariusz Lemańczyk
Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland
Email: mlem@mat.umk.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11872-1
PII: S 0002-9939(2013)11872-1
Received by editor(s): February 2, 2012
Published electronically: August 8, 2013
Communicated by: Nimish Shah
Article copyright: © Copyright 2013 By the authors