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Zbl 0624.10040
Schatte, Peter
Some estimates of the $H\sb{\infty}$-uniform distribution.
(English)
[J] Monatsh. Math. 103, 233-240 (1987). ISSN 0026-9255; ISSN 1436-5081/e

The sequences $(y\sb n)=(a+b \log n+\epsilon\sb n)$ are uniformly distributed in the sense of the summation method $H\sb{\infty}$. In the present paper the speed of convergence of this procedure is estimated for these sequences and for some other sequences. For the sequences $(a+b \log n)$ the $H\sb{\infty}$-means converge considerably faster than logarithmic means.
MSC 2000:
*11K06 General theory of distribution modulo 1
40G99 Special methods of summability

Keywords: H${}\sb{\infty }$-uniform distribution; summation method $H\sb{\infty }$; speed of convergence; $H\sb{\infty }$-means

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