On a characterization theorem on Abelian groups

• Autores: Gennadiy Feldman, Margaryta Myronyuk
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 77, Fasc. 3-4, 2010, págs. 383-398
• Idioma: inglés
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• Resumen

  • Year: 2010 Vol.: 77 Fasc.: 3-4 Title: On a characterization theorem on Abelian groups Author(s): Gennadiy Feldman and Margaryta Myronyuk Let »1; »2; : : : ; »n; n ¸ 2 be independent identically distributed random variables.

    It is well known that if ¹» = 1 n Pn j=1 »j and v = (»1¡ ¹»; »2¡ ¹»; : : : ; »n¡ ¹») are indepen- dent, then all »j are Gaussian. We give a complete description of second countable locally compact Abelian groups for which a group analogue of this characterization theorem holds true.

    Address:

    Gennadiy Feldman Mathematical Division B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine 47, Lenin Ave, Kharkov, 61103 Ukraine Address:

    Margaryta Myronyuk Mathematical Division B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine 47, Lenin Ave, Kharkov, 61103 Ukraine