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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On multiplicative conditionally free convolution


Authors: Mihai Popa and Jiun-Chau Wang
Journal: Trans. Amer. Math. Soc. 363 (2011), 6309-6335
MSC (2000): Primary 46L53; Secondary 05A18, 60E07
Published electronically: June 27, 2011
MathSciNet review: 2833556
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Abstract: Using the combinatorics of non-crossing partitions, we construct a conditionally free analogue of Voiculescu's $ S$-transform. The result is applied to the analytical description of conditionally free multiplicative convolution and the characterization of infinite divisibility.


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Additional Information

Mihai Popa
Affiliation: Department of Mathematics, Indiana University at Bloomington, Rawles Hall, 831 E 3rd Street, Bloomington, Indiana 47405
Email: mipopa@indiana.edu

Jiun-Chau Wang
Affiliation: Department of Mathematics and Statistics, Queen’s University, Jeffery Hall, Kingston, Ontario, Canada K7M 7H7
Email: jiuwang@mast.queensu.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05242-6
PII: S 0002-9947(2011)05242-6
Keywords: Conditionally free independence, multiplicative convolution, $S$-transform, infinite divisibility, non-crossing and non-crossing linked partitions.
Received by editor(s): May 29, 2008
Received by editor(s) in revised form: June 23, 2009, and October 20, 2009
Published electronically: June 27, 2011
Additional Notes: The first author was partially supported by the grant 2-CEx06-11-34 of the Romanian Government
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.