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On orthogonality of Riesz products

Published online by Cambridge University Press:  24 October 2008

Gavin Brown  and
William Moran
Gavin Brown
Affiliation:
Department of Pure Mathematics, University of Liverpool
William Moran
Affiliation:
Department of Pure Mathematics, University of Liverpool
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Extract

A typical Riesz product on the circle is the weak* limit

where – 1 ≤ rk ≤ 1, øk ∈ R, λT is Haar measure, and the positive integers nk satisfy nk+1/nk ≥ 3. A classical result of Zygmund (11) implies that either µ is absolutely continuous with respect to λT (when ) or µ is purely singular (when ).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 173 - 181
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

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