TY - JOUR

T1 - The wiener lemma and cocycles

AU - Rychlik, Marek Ryszard

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1988/11/1

Y1 - 1988/11/1

N2 - 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.

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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U2 - 10.1090/S0002-9939-1988-0964876-6

DO - 10.1090/S0002-9939-1988-0964876-6

M3 - Article

AN - SCOPUS:84968482073

VL - 104

SP - 787

EP - 792

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -