Weighted Means, Strict Ergodicity, and Uniform Distributions |
| |
Authors: | V V Kozlov |
| |
Institution: | (1) V. A. Steklov Mathematics Institute, Russian Academy of Sciences, Moscow, Russia |
| |
Abstract: | We strengthen the well-known Oxtoby theorem for strictly ergodic transformations by replacing the standard Cesaro convergence by the weaker Riesz or Voronoi convergence with monotonically increasing or decreasing weight coefficients. This general result allows, in particular, to strengthen the classical Weyl theorem on the uniform distribution of fractional parts of polynomials with irrational coefficients. |
| |
Keywords: | Weyl theorem Cesaro and Voronoi convergences Borel measure Oxtoby's theorem strictly ergodic transformation Riesz summation method |
本文献已被 SpringerLink 等数据库收录! |
|