On regularity for measures in multiplicative free convolution semigroups
Abstract
Given a probability measure μ on the real line, there exists a semigroup μt with real parameter t>1 which interpolates the discrete semigroup of measures μn obtained by iterating its free convolution. It was shown in [BB2004] that it is impossible that μt 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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