Proceedings of the American Mathematical Society

Author(s): Youngho Ahn; Geon Ho Choe
Journal: Proc. Amer. Math. Soc. 128 (2000), 503-510.
MSC (1991): Primary 28D05, 47A35
Posted: June 21, 1999
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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

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.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 28D05, 47A35

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: 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
Posted: 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
Copyright of article: Copyright 1999, American Mathematical Society

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