Resumen de On a characterization theorem on Abelian groups

Gennadiy Feldman, Margaryta Myronyuk

• 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