Dani, S. G. ; McCrudden, M. (2007) Convolution roots and embeddings of probability measures on lie groups Advances in Mathematics, 209 (1). pp. 198211. ISSN 00018708

PDF
 Publisher Version
187kB 
Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00018...
Related URL: http://dx.doi.org/10.1016/j.aim.2006.05.002
Abstract
We show that for a large class of connected Lie groups G, viz. from class C described below, given a probability measure μ on G and a natural number n, for any sequence {v_{i}} of th convolution roots of μ there exists a sequence {z_{i}} of _{n}th elements of G, centralising the support of μ , and such that {Z_{i}ν _{i}Z_{i}^{1}}is relatively compact; thus the set of roots is relatively compact 'modulo' the conjugation action of the centraliser of suppµ. We also analyse the dependence of the sequence {z_{i}} on n. The results yield a simpler and more transparent proof of the embedding theorem for infinitely divisible probability measures on the Lie groups as above, proved in [S.G. Dani, M. McCrudden, Embeddability of infinitely divisible distributions on linear Lie groups, Invent. Math. 110 (1992) 237261].
Item Type:  Article 

Source:  Copyright of this article belongs to Elsevier Science. 
Keywords:  Probability Measures; Convolution Roots; Infinite Divisibility; Embedding 
ID Code:  8240 
Deposited On:  26 Oct 2010 12:06 
Last Modified:  16 May 2016 18:17 
Repository Staff Only: item control page