Absolutely continuous spectrum of some group extensions of Gaussian actions

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January 2010, 26(1): 365-378. doi: 10.3934/dcds.2010.26.365

Absolutely continuous spectrum of some group extensions of Gaussian actions

1.	Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland

Received February 2009 Revised July 2009 Published October 2009

Abstract
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Group extensions of Gaussian $\mathbb{G}$-actions with absolutely continuous spectrum in the orthocomplement of the functions depending on the first coordinate are constructed for $\mathbb{G}$ equal to $\mathbb{Z}^{d}$, $d\in\mathbb{N}\cup\{\infty\}$ or $\mathbb{Q}$.

Keywords: absolutely continuous spectrum., Gaussian actions, cocycles.

Mathematics Subject Classification: Primary: 37A15, 37A20; Secondary: 60G1.

Citation: Dariusz Skrenty. Absolutely continuous spectrum of some group extensions of Gaussian actions. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 365-378. doi: 10.3934/dcds.2010.26.365

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