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ANZAI SKEW PRODUCTS WITH LEBESGUE COMPONENT OF INFINITE MULTIPLICITY

Published online by Cambridge University Press:  01 March 1997

A. IWANIK
Affiliation:
Institute of Mathematics, Technical University of Wrocław, 50–370 Wrocław, Poland
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Abstract

Let f be a 1-periodic C1-function whose Fourier coefficients satisfy the condition [sum ]n[mid ]n[mid ]3[mid ] fˆ(n[mid ]2<∞. For every α∈R\Q and mZ\{0}, we consider the Anzai skew product T(x, y) = (x+α, y+mx+f(x)) acting on the 2-torus. It is shown that T has infinite Lebesgue spectrum on the orthocomplement L2(dx) of the space of functions depending only on the first variable. This extends some earlier results of Kushnirenko, Choe, Lemańczyk, Rudolph, and the author.

Type
Research Article
Copyright
© The London Mathematical Society 1997

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