The S-transform of symmetric probability measures with unbounded supports

The S-transform of symmetric probability measures with unbounded supports
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具有无界支持的对称概率测度的 S 变换

DOI：
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发表时间：
2009
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通讯作者：
V. Pérez
V. Pérez
中科院分区：
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文献类型：
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作者：
E. OctavioArizmendi;V. Pérez

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Voiculescu S 变换是一种用于计算概率度量的自由乘法卷积的分析工具。已经研究了具有非负支持的概率测度和具有所有矩和零均值的概率测度。我们将 S 变换扩展到具有无界支持且无矩的对称概率测度。作为一种应用，对称自由稳定测度的表示被导出为半圆测度与正自由稳定测度的乘法卷积。
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.