Abstract
This note extends Voiculescu's $S$-transform based analytical machinery for free multiplicative convolution to the case where the mean of the probability measures vanishes. We show that with the right interpretation of the $S$-transform in the case of vanishing mean, the usual formula makes perfectly good sense.
Citation
N. Raj Rao. Roland Speicher. "Multiplication of free random variables and the S-transform: the case of vanishing mean." Electron. Commun. Probab. 12 248 - 258, 2007. https://doi.org/10.1214/ECP.v12-1274
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