This article is cited in 1 paper

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

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.

UDC: 517.9

Received: 12.04.2004

DOI: 10.4213/faa17

 English version: Functional Analysis and Its Applications, 2006, 40:1, 34–41

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