Russian Mathematical Surveys 60(6), pp. 1121-1146.
ISSN/ISBN: 0036-0279 DOI: 10.1070/RM2005v060n06ABEH004284
Abstract: A circle of problems related to the application of the Riesz and Voronoi summation methods in ergodic theory, number theory, and probability theory is considered. The first digit paradox is discussed, strengthenings of the classical result of Weyl on the uniform distribution of the fractional parts of the values of a polynomial are indicated, and the possibility of sharpening the Birkhoff-Khinchin ergodic theorem is considered. In conclusion, some unsolved problems are listed.
Bibtex:
@article{,
title={Weighted averages, uniform distribution, and strict ergodicity},
author={Kozlov, Valerii V},
journal={Russian Mathematical Surveys},
volume={60},
number={6},
pages={1121},
year={2005},
publisher={IOP Publishing},
ISSN={0036-0279},
DOI={10.1070/RM2005v060n06ABEH004284},
}
Reference Type: Journal Article
Subject Area(s): Analysis, Dynamical Systems