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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 14, Fasc. 2,
pages 327 - 345
 

DOMAINS OF ATTRACTION OF STABLE MEASURES ON THE HEISENBERG GROUP

Hans-Peter Scheffler

Abstract: Let H d be the (2d+ l) -dimensional Heisenberg group and (m) tt>0 be a continuous convolution semigroup of probability measures on H . d Let moreover m 1 be full. A probability measure n is said to belong to the domain of attraction of m 1 if there exists a sequence (s ) nn of automorphisms of H d such that s nn --> m n 1 weakly. We prove some simple necessary and sufficient conditions on n for the existence of such automorphisms if (m ) tt>0 has no Gaussian component. Furthermore, the domain of normal attraction of a Gaussian measure on H d is considered.

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

Key words and phrases: -

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