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Weighted means, strict ergodicity, and uniform distributions. (English. Russian original) Zbl 1121.37009
Math. Notes 78, No. 3, 329-337 (2005); translation from Mat. Zametki 78, No. 3, 358-367 (2005).
Author’s summary: We strengthen the well-known Oxtoby theorem for strictly ergodic transformations by replacing the standard Cesàro 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 polynomial with irrational coefficient.

MSC:
37A30 Ergodic theorems, spectral theory, Markov operators
37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010)
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
40G99 Special methods of summability
11K06 General theory of distribution modulo \(1\)
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