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Ergodic measures for the irrational rotation on the circle

Part of: Harmonic analysis in one variable Measure-theoretic ergodic theory

Published online by Cambridge University Press:  09 April 2009

William Moran
William Moran
Affiliation:
Department of Pure MathematicsThe University of AdelaideAdelaide, South Australia 5000, Australia
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Abstract

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Riesz products are employed to give a construction of quasi-invariant ergodic measures under the irrational rotation of T. By suitable choice of the parameters such measures may be required to have Fourier-Stieltjes coefficients vanishing at infinity. We show further that these are the unique quasi-invariant measures on T with their associated Radon-Nikodym derivative.

MSC classification

Secondary: 28D99: None of the above, but in this section 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 1 , August 1988 , pp. 133 - 141
Copyright
Copyright © Australian Mathematical Society 1988

References

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