The wiener lemma and cocycles

Marek Ryszard Rychlik

doi:10.1090/S0002-9939-1988-0964876-6

The wiener lemma and cocycles

Marek Ryszard Rychlik

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We giv;…ufficient and necessary condition fo;…unction with its values in the unit circle to b;…ultiplicative coboundary. This theorem generalizes the following result of Veech [1]. Let T;…#x2192;……otation of the unit circl;…y an irrational angle θ. Let F;…#x2192;……easuable function. The;……ultiplicative coboundary iff ∫_T F(x)F(Tx) ……T^n-1x)dμ(x) → 1, as ||nθ|| → θ where ||no|| is the distance of no from integers an;…s the Haar measure.

Original language	English (US)
Pages (from-to)	787-792
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	104
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-1988-0964876-6
State	Published - Nov 1 1988
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-1988-0964876-6

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abstract = "We giv;…ufficient and necessary condition fo;…unction with its values in the unit circle to b;…ultiplicative coboundary. This theorem generalizes the following result of Veech [1]. Let T;…#x2192;……otation of the unit circl;…y an irrational angle θ. Let F;…#x2192;……easuable function. The;……ultiplicative coboundary iff ∫T F(x)F(Tx) ……Tn-1x)dμ(x) → 1, as ||nθ|| → θ where ||no|| is the distance of no from integers an;…s the Haar measure.",

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AB - We giv;…ufficient and necessary condition fo;…unction with its values in the unit circle to b;…ultiplicative coboundary. This theorem generalizes the following result of Veech [1]. Let T;…#x2192;……otation of the unit circl;…y an irrational angle θ. Let F;…#x2192;……easuable function. The;……ultiplicative coboundary iff ∫T F(x)F(Tx) ……Tn-1x)dμ(x) → 1, as ||nθ|| → θ where ||no|| is the distance of no from integers an;…s the Haar measure.

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The wiener lemma and cocycles

Abstract

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