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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 13, Fasc. 1,
pages 33 - 37
 

ON THE CLASS OF OPERATOR STABLE DISTRIBUTIONS IN A SEPARABLE BANACH SPACE

Gerhard Siegel

Abstract: This paper characterizes the class of all limit probability measures m of normalized and centralized convolution powers in a separable Banach space E which are defined by

A n*n *d -w--> m u xn
for some linear and bounded operators An and some shifts xn (- E. It is shown that this class coincides with the set of all infinitely divisible laws in E provided that E is infinite dimensional.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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