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Spectral types of skewed Bernoulli shift

Authors:	Youngho Ahn Geon Ho Choe

Institution:	Korea Advanced Institute of Science and Technology, Kusong-dong, Yusong-gu, 305-701 Taejon, Korea ; Korea Advanced Institute of Science and Technology, Kusong-dong, Yusong-gu, 305-701 Taejon, Korea

Abstract:	For the transformation $T: x \mapsto kx \pmod 1$ for $k \geq 2$ , it is proved that a real-valued function of modulus is not a multiplicative coboundary if the discontinuities $0 < x_1< \cdots < x_n \leq 1$ of are -adic points and $x_1 \ge \frac 1k$ . It is also proved that the weakly mixing skew product transformations arising from Bernoulli shifts have Lebesgue spectrum.

Keywords:	Coboundary metric density weakly mixing Lebesgue spectrum Bernoulli shift

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