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arXiv · 1112.2783

On regularity for measures in multiplicative free convolution semigroups

Ping Zhong
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Abstract

Given a probability measure $μ$ on the real line, there exists a semigroup $μ_t$ with real parameter $t>1$ which interpolates the discrete semigroup of measures $μ_n$ obtained by iterating its free convolution. It was shown in \cite{[BB2004]} that it is impossible that $μ_t$ has no mass in an interval whose endpoints are atoms. We extend this result to semigroups related to multiplicative free convolution. The proofs use subordination results.

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Ping Zhong. 2012-10-22. On regularity for measures in multiplicative free convolution semigroups. https://arxiv.org/abs/1112.2783

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