Free Brownian motion and free convolution semigroups: multiplicative case

Ping Zhong

We consider a pair of probability measures $\mu ,\nu$ on the unit circle such that ${\Sigma }_{\lambda }({\eta }_{\nu }(z))=z/{\eta }_{\mu }(z)$. We prove that the same type of equation holds for any $t\ge 0$ when we replac…