Absolutely continuous spectrum of some group extensions of Gaussian actions

Dariusz Skrenty

doi:10.3934/dcds.2010.26.365

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2010, Volume 26, Issue 1: 365-378. Doi: 10.3934/dcds.2010.26.365

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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

Received: January 31, 2009

Revised: June 30, 2009

Published: February 2010

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Abstract

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 $\mathbb{Q}$.

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Mathematics Subject Classification: Primary: 37A15, 37A20; Secondary: 60G15.

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