A note on weakly mixing functions

Author:
S. Glasner

Journal:
Proc. Amer. Math. Soc. **78** (1980), 124-126

MSC:
Primary 54H20; Secondary 28D05

DOI:
https://doi.org/10.1090/S0002-9939-1980-0548098-1

MathSciNet review:
548098

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Abstract: Every almost periodic function is the uniform limit of polynomials of weakly mixing functions. If and are uniformly closed translation invariant algebras of purely weakly mixing functions and almost periodic functions respectively, and is the algebra generated by and , then every weakly mixing function in belongs to .

**[1]**H. Furstenberg,*Disjointness in ergodic theory, minimal sets and a problem in Diophantine approximation*, Math. Systems Theory**1**(1967), 1-49. MR**0213508 (35:4369)****[2]**R. Ellis,*Lectures on topological dynamics*, Benjamin, New York, 1969. MR**0267561 (42:2463)****[3]**R. Ellis and S. Glasner,*Pure weak mixing*, Trans. Amer. Math. Soc.**243**(1978), 135-146. MR**0494022 (58:12961)****[4]**A. Knapp,*Functions behaving like almost automorphic functions*, Topological Dynamics, (Symposium, Colorado State Univ., Ft. Collins, Colo., 1967), Benjamin, New York, 1968, pp. 299-317. MR**0238294 (38:6570)****[5]**R. Peleg,*Some extensions of weakly mixing flows*, Israel J. Math.**9**(1971), 330-336. MR**0281184 (43:6903)****[6]**W. A. Veech, Private communication.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1980-0548098-1

Keywords:
Weakly mixing functions,
almost periodic functions,
purely weakly mixing functions

Article copyright:
© Copyright 1980
American Mathematical Society