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The Voiculescu S 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 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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Arizmendi et al. (2009) studied this question.
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