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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

Dariusz Skrenty 1,

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

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