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The Union of Ur-sets for the Characters System of the Group of p-adic Integers

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Abstract

The following theorem is proved: the union of countably many closed Ur-sets (r > 2) for the Vilenkin-Dzhafarli system is again a Ur-set for this system.

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References

  1. G. A. Agaev, N. I. Vilenkin, G. M. Jafarli, and A. I. Rubinstein, Multiplicative Function Systems and Harmonic Analysis on Groups with Zero Measure (Elm, Baku, 1981) [in Russian].

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  2. T. D. Kozlovskaya, “The U p-Sets for the Walsh Function System,” Vestnik MSTU “Stankin,” No 1(18), 85 (2012).

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  3. V. A. Skvortsov and F. Tulone, “Kurzweil-Henstock Type Integral on Zero-Dimensional Group and Some of its Applications,” Czechoslovak Math. J. 58, 1167 (2008).

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  4. V. A. Skvortsov, “On Mo-Sets for Series with Respect to Characters of Compact Zero-Dimensional Group,” Tatra Mt. Math. Publ. 62, 165 (2014).

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  5. A. Zygmund, Trigonometric Series, Vol. 1 (Cambridge Univ. Press, Cambridge, 2011; Mir, Moscow, 1965).

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Acknowledgments

The author is grateful to Prof. V. A. Skvortsov for formulation of the problem and assistance in the work.

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Authors and Affiliations

  1. Moscow State University of Technology “Stankin,”, Vadkovsky lane, 3a, Moscow, 127055, Russia

    T. D. Kozlovskaya

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  1. T. D. Kozlovskaya
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Correspondence to T. D. Kozlovskaya.

Additional information

Russian Text © The Author(s). 2019. published in Vestnik Moskovskogo Universiteta. Matematika. Mekhanika. 2019. Vol. 74, No. 4, pp. 42–46.

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Kozlovskaya, T.D. The Union of Ur-sets for the Characters System of the Group of p-adic Integers. Moscow Univ. Math. Bull. 74, 159–162 (2019). https://doi.org/10.3103/S0027132219040041

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  • DOI: https://doi.org/10.3103/S0027132219040041

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