A. L. Rukhin, “On a theorem of S. N. Bernshtein”, Mat. Zametki, 6:3 (1969), 301–307; Math. Notes, 6:3 (1969), 638

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Matematicheskie Zametki, 1969, Volume 6, Issue 3, Pages 301–307 (Mi mzm6936)

This article is cited in 11 scientific papers (total in 11 papers)

On a theorem of S. N. Bernshtein

A. L. Rukhin

Leningrad Department of V. A. Steklov Institute of Mathematics, USSR Academy of Sciences

Full-text PDF (504 kB) Citations (11)

Abstract: This note contains the proof of a theorem on the characterization of a normal law on locally compact Abelian groups, this theorem being a generalization of S. N. Bernshtein's wellknown characterization of the normal law by the property that sums and differences of two independent random variables are also random variables.

Received: 11.10.1967

English version:
Mathematical Notes, 1969, Volume 6, Issue 3, Pages 638–641
DOI: https://doi.org/10.1007/BF01119683

Bibliographic databases:

UDC: 519.2

Language: Russian

Citation: A. L. Rukhin, “On a theorem of S. N. Bernshtein”, Mat. Zametki, 6:3 (1969), 301–307; Math. Notes, 6:3 (1969), 638–641

Citation in format AMSBIB

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\by A.~L.~Rukhin

\paper On a~theorem of S.\,N.~Bernshtein

\jour Mat. Zametki

\yr 1969

\vol 6

\issue 3

\pages 301--307

\mathnet{http://mi.mathnet.ru/mzm6936}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=253455}

\zmath{https://zbmath.org/?q=an:0195.20301|0184.22604}

\transl

\jour Math. Notes

\yr 1969

\vol 6

\issue 3

\pages 638--641

\crossref{https://doi.org/10.1007/BF01119683}

Linking options:

https://www.mathnet.ru/eng/mzm6936

https://www.mathnet.ru/eng/mzm/v6/i3/p301

This publication is cited in the following 11 articles:

L. B. Klebanov, “Kharakterizatsii veroyatnostnykh raspredelenii svoistvami lineinykh form so sluchainymi koeffitsientami”, Veroyatnost i statistika. 30, Zap. nauchn. sem. POMI, 501, POMI, SPb., 2021, 181–193
Gennadiy Feldman, “The Kac–Bernstein functional equation on Abelian groups”, Aequat. Math., 95:4 (2021), 737
E. I. Zelenov, “ $p$ -Adic Gaussian Random Variables”, Proc. Steklov Inst. Math., 306 (2019), 120–126
G. M. Feldman, “Independent random variables on Abelian groups with independent sum and difference”, Theory Probab. Appl., 61:2 (2017), 335–345
G. M. Feldman, “Gaussian measures in the sence of Bernstein: factorization, supports, zero-one law”, Theory Probab. Appl., 56:3 (2011), 359–375
Feldman G.M., “Gaussovskie raspredeleniya v smysle bernshteina na lokalno kompaktnykh abelevykh gruppakh”, Doklady Akademii nauk, 440:3 (2011), 314–316
G. M. Feldman, “Gaussian distributions in the sense of Bernstein on locally compact Abelian groups”, Dokl. Math., 84:2 (2011), 653
GENNADIY FELDMAN, PIOTR GRACZYK, “THE SKITOVICH–DARMOIS THEOREM FOR LOCALLY COMPACT ABELIAN GROUPS”, J. Aust. Math. Soc., 88:3 (2010), 339
M. V. Mironyuk, G. M. Feldman, “On a characterization theorem on finite Abelian groups”, Siberian Math. J., 46:2 (2005), 315–324
G. M. Feldman, “More on the Skitovich–Darmous theorem for finite Abelian groups”, Theory Probab. Appl., 45:3 (2001), 507–511
G. M. Feldman, “Gaussian distributions on locally compact Abelian groups”, Funct. Anal. Appl., 11:1 (1977), 76–78

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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