On the self-similarity problem for Gaussian-Kronecker flows
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- by Krzysztof Fra̧czek, Joanna Kułaga and Mariusz Lemańczyk PDF
- Proc. Amer. Math. Soc. 141 (2013), 4275-4291
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.References
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Additional Information
- Krzysztof Fra̧czek
- 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
- MR Author ID: 977686
- 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
- MR Author ID: 112360
- Email: mlem@mat.umk.pl
- Received by editor(s): February 2, 2012
- Published electronically: August 8, 2013
- Communicated by: Nimish Shah
- © Copyright 2013 By the authors
- Journal: Proc. Amer. Math. Soc. 141 (2013), 4275-4291
- MSC (2010): Primary 37A10, 60G15; Secondary 43A05, 43A46, 37A50, 37A45
- DOI: https://doi.org/10.1090/S0002-9939-2013-11872-1
- MathSciNet review: 3105870