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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spectral types of skewed Bernoulli shift


Authors: Youngho Ahn and Geon Ho Choe
Journal: Proc. Amer. Math. Soc. 128 (2000), 503-510
MSC (1991): Primary 28D05, 47A35
Published electronically: June 21, 1999
MathSciNet review: 1622769
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Abstract: For the transformation $T: x \mapsto kx \pmod 1$ for $k \geq 2 $, it is proved that a real-valued function $f(x)$ of modulus $1$ is not a multiplicative coboundary if the discontinuities $0 < x_1< \cdots < x_n \leq 1$ of $f(x)$ are $k$-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.


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Additional Information

Youngho Ahn
Affiliation: Korea Advanced Institute of Science and Technology, Kusong-dong, Yusong-gu, 305-701 Taejon, Korea
Email: ahntau@math.kaist.ac.kr

Geon Ho Choe
Affiliation: Korea Advanced Institute of Science and Technology, Kusong-dong, Yusong-gu, 305-701 Taejon, Korea
Email: choe@euclid.kaist.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04990-4
PII: S 0002-9939(99)04990-4
Keywords: Coboundary, metric density, weakly mixing, Lebesgue spectrum, Bernoulli shift
Received by editor(s): July 25, 1997
Received by editor(s) in revised form: March 31, 1998
Published electronically: June 21, 1999
Additional Notes: The second author’s research was supported by GARC-SRC and KOSEF 95-07-01-02-01-3
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1999 American Mathematical Society