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Kalyabin, G. A.

On existence conditions for sequences uniformly distributed with respect to Voronoi’s methods. (English. Russian original) Zbl 1172.40003

Dokl. Math. 76, No. 1, 494-496 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 415, No. 1, 18-20 (2007).
Sequences that are uniformly distributed with respect to some summation methods are investigated. It is proved that there is a Voronoi summation method such that there is no uniformly distributed sequence with respect to this summation method.
Reviewer: Ferenc Weisz (Budapest)

Cited in 1 Review

MSC:

40G99 Special methods of summability

Keywords:

uniformly distributed sequence; Voronoi summation
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\textit{G. A. Kalyabin}, Dokl. Math. 76, No. 1, 494--496 (2007; Zbl 1172.40003); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 415, No. 1, 18--20 (2007)
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References:

[1] V. V. Kozlov, Usp. Mat. Nauk 60(6(336)), 115–138 (2006).
[2] G. H. Hardy, Divergent Series, 2nd ed. (Clarendon Press, Oxford, 1956; Russian transl. of 1st ed.: Inostrannaya Literatura, Moscow, 1951). · Zbl 0897.01044
[3] L. Kuipers and G. Niderreiter, Uniform Distribution of Sequences (Wiley, New York, 1974; Nauka, Moscow, 1985).
[4] E. V. Gordelii, Vestn. Mosk. Univ., Ser. 1: Mat. Mekh., No. 6, 18–24 (2004).
[5] G. A. Kalyabin, Dokl. Math. 74, 635–636 (2006) [Dokl. Akad. Nauk 410, 19–20 (2006)]. · Zbl 1136.11048
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