English

On regularity for measures in multiplicative free convolution semigroups

Functional Analysis 2015-03-19 v2

Abstract

Given a probability measure μ\mu on the real line, there exists a semigroup μt\mu_t with real parameter t>1t>1 which interpolates the discrete semigroup of measures μn\mu_n obtained by iterating its free convolution. It was shown in \cite{[BB2004]} that it is impossible that μt\mu_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.

Keywords

Cite

@article{arxiv.1112.2783,
  title  = {On regularity for measures in multiplicative free convolution semigroups},
  author = {Ping Zhong},
  journal= {arXiv preprint arXiv:1112.2783},
  year   = {2015}
}

Comments

Some typos fixed, accepted by Complex Analysis and Operator Theory

R2 v1 2026-06-21T19:50:17.186Z