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

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- by Octavio Arizmendi E. and Victor Pérez-Abreu PDF
- Proc. Amer. Math. Soc.
**137**(2009), 3057-3066 Request permission

## 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.## References

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## Additional Information

**Octavio Arizmendi E.**- Affiliation: School of Mathematics, University of Guanajuato, Valenciana, Guanajuato, GTO 36240, Mexico
- Email: octavius@cimat.mx
**Victor Pérez-Abreu**- Affiliation: Research Center for Mathematics, CIMAT, Apartado Postal 402, Guanajuato, GTO 36000, Mexico
- Email: pabreu@cimat.mx
- 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
- © Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**137**(2009), 3057-3066 - MSC (2000): Primary 46L54, 15A52
- DOI: https://doi.org/10.1090/S0002-9939-09-09841-4
- MathSciNet review: 2506464