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The $ S$-transform of symmetric probability measures with unbounded supports

Authors: Octavio Arizmendi E. and Victor Pérez-Abreu
Journal: Proc. Amer. Math. Soc. 137 (2009), 3057-3066
MSC (2000): Primary 46L54, 15A52
Published electronically: February 16, 2009
MathSciNet review: 2506464
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Abstract: The Voiculescu $ S$-transform is an analytic tool for computing free multiplicative convolutions of probability measures. It has been studied for probability measures with non-negative support and for probability measures having all moments and zero mean. We extend the $ S$-transform to symmetric probability measures with unbounded support and without moments. As an application, a representation of symmetric free stable measures is derived as a multiplicative convolution of the semicircle measure with a positive free stable measure.

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Additional Information

Octavio Arizmendi E.
Affiliation: School of Mathematics, University of Guanajuato, Valenciana, Guanajuato, GTO 36240, Mexico

Victor Pérez-Abreu
Affiliation: Research Center for Mathematics, CIMAT, Apartado Postal 402, Guanajuato, GTO 36000, Mexico

Keywords: Multiplicative convolution, free stable distribution, random matrix
Received by editor(s): September 29, 2008
Received by editor(s) in revised form: November 18, 2008
Published electronically: February 16, 2009
Additional Notes: The first author’s research was supported by SNI-CONACYT Grant A. I. 4337 and the Statistics Laboratory of CIMAT
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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