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Funktsional'nyi Analiz i ego Prilozheniya, 2006, Volume 40, Issue 1, Pages 43–51
DOI: https://doi.org/10.4213/faa17 (Mi faa17) 		 
This article is cited in 2 scientific papers (total in 2 papers)

A Sharp Estimate for the Rate of Convergence in Mean of Birkhoff Sums for Some Classes of Periodic Differentiable Functions

A. V. Rozhdestvenskii

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (204 kB) Citations (2)
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DOI: https://doi.org/10.4213/faa17
Abstract: For a badly approximable vector $\alpha$, we obtain a sharp estimate for the rate of convergence in the space $L_p$ ($0<p<\infty$) of the Birkhoff means $\frac1{n}\sum_{s=0}^{n-1} f(x+s\alpha)$ for an absolutely continuous periodic function $f$ and for functions in spaces of Bessel potentials.
Keywords: Birkhoff sum, badly approximable vector, generalized Bessel potential.
Received: 12.04.2004
English version:
Functional Analysis and Its Applications, 2006, Volume 40, Issue 1, Pages 34–41
DOI: https://doi.org/10.1007/s10688-006-0004-5
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. V. Rozhdestvenskii, “A Sharp Estimate for the Rate of Convergence in Mean of Birkhoff Sums for Some Classes of Periodic Differentiable Functions”, Funktsional. Anal. i Prilozhen., 40:1 (2006), 43–51; Funct. Anal. Appl., 40:1 (2006), 34–41
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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