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Mat. Zametki, 2005, Volume 78, Issue 3, Pages 358–367 (Mi mz2594)  

This article is cited in 5 scientific papers (total in 5 papers)

Weighted Means, Strict Ergodicity, and Uniform Distributions

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences

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.

DOI: https://doi.org/10.4213/mzm2594

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English version:
Mathematical Notes, 2005, 78:3, 329–337

Bibliographic databases:

Document Type: Article
UDC: 519.21
Received: 31.03.2005

Citation: V. V. Kozlov, “Weighted Means, Strict Ergodicity, and Uniform Distributions”, Mat. Zametki, 78:3 (2005), 358–367; Math. Notes, 78:3 (2005), 329–337

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Kozlov, “Weighted averages, uniform distribution, and strict ergodicity”, Russian Math. Surveys, 60:6 (2005), 1121–1146  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Accardi L., Mukhamedov F., “A note on noncommutative unique ergodicity and weighted means”, Linear Algebra Appl., 430:2-3 (2009), 782–790  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    3. V. V. Kozlov, “On Bohl's Argument Theorem”, Math. Notes, 93:1 (2013), 83–89  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Duvenhage R., Mukhamedov F., “Relative Ergodic Properties of C-Dynamical Systems”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 17:1 (2014), 1450005  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Duvenhage R., Mukhamedov F., “a Few Remarks on Relative Ergodic Properties of C-Dynamical Systems”, International Conference on Mathematics, Engineering and Industrial Applications 2014 (Icomeia 2014), AIP Conference Proceedings, 1660, eds. Ramli M., Junoh A., Roslan N., Masnan M., Kharuddin M., Amer Inst Physics, 2015, 050019  crossref  isi  scopus  scopus
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