Skip to main content
SpringerLink
Log in

On the Heyde theorem for some locally compact Abelian groups

  • Mathematics
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

According to the well-known Heyde theorem Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form in n independent random variables given another. For n = 2 we prove analogs of this theorem in the case when random variables take values in a locally compact Abelian group X, and coefficients of the linear forms are topological automorphisms of the group X.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C. C. Heyde, Sankhya Ser. A 32, 115–118 (1970).

    MathSciNet  Google Scholar 

  2. A. M. Kagan, Yu. V. Linnik, and S. R. Rao, Characterization Problems in Mathematical Statistics (Nauka, Moscow, 1972; Wiley, New York, 1973).

    MATH  Google Scholar 

  3. G. M. Feldman, J. Theor. Probab. 17, 929–941 (2004).

    Article  Google Scholar 

  4. M. V. Mironyuk and G. M. Feldman, Sib. Math. J. 46, 315–324 (2005).

    Article  Google Scholar 

  5. G. M. Feldman, Probab. Theory Relat. Fields 133, 345–357 (2005).

    Article  Google Scholar 

  6. G. M. Feldman, Stud. Math. 177, 67–79 (2006).

    Article  Google Scholar 

  7. G. M. Feldman, J. Funct. Anal. 258, 3977–3987 (2010).

    Article  MathSciNet  Google Scholar 

  8. M. V. Myronyuk, J. Aust. Math. Soc. 88, 93–102 (2010).

    Article  MathSciNet  Google Scholar 

  9. G. M. Feldman, Math. Nachr. 286, 340–348 (2013).

    Article  MathSciNet  Google Scholar 

  10. M. V. Myronyuk, Colloquium Math. 132, 195–210 (2013).

    Article  MathSciNet  Google Scholar 

  11. G. M. Feldman, Functional Equations and Characterization Problems on Locally Compact Abelian Groups, EMS Tracts in Mathematics, Vol. 5 (Eur. Math. Soc., Zurich, 2008).

    Google Scholar 

  12. K. R. Parthasarathy, Probability Measures on Metric Spaces (Academic, New York, 1967).

    Book  MATH  Google Scholar 

  13. G. M. Feldman, Theory Probab. Appl. 45, 507–511 (2001).

    Article  Google Scholar 

  14. G. M. Feldman, Publ. Math. Debrecen 87, 147–166 (2015).

    Article  MathSciNet  Google Scholar 

  15. G. M. Feldman, Theory Probab. Appl. 22, 133–140 (1977).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Kharkov, 61103, Ukraine

    G. M. Feldman

Authors
  1. G. M. Feldman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. M. Feldman.

Additional information

Published in Russian in Doklady Akademii Nauk, 2017, Vol. 473, No. 3, pp. 16–20.

The article was translated by the author.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Feldman, G.M. On the Heyde theorem for some locally compact Abelian groups. Dokl. Math. 95, 147–150 (2017). https://doi.org/10.1134/S1064562417020119

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562417020119

Search

Navigation