zbMATH — the first resource for mathematics

Uniform distribution on a torus. (Russian, English) Zbl 1076.37500
Vestn. Mosk. Univ., Ser. I 2004, No. 2, 22-29 (2004); translation in Mosc. Univ. Math. Bull. 59, No. 2, 23-31 (2004).
The author establishes conditions for uniform distributions of smooth motions on multidimensional tori in the case when the Cesàro means are replaced by the means of a more general form. Continuous analogues of the inclusion and equivalence theorems are proved for the Riesz means. The conditions of sign-definiteness and oscillation are established for the integrals with the weight from conditionally periodic functions.

37A05 Dynamical aspects of measure-preserving transformations
28D10 One-parameter continuous families of measure-preserving transformations
37A30 Ergodic theorems, spectral theory, Markov operators
37A50 Dynamical systems and their relations with probability theory and stochastic processes