摘要
In this paper, we study the supports of measures in the free additive convolution semigroup {μ □t : t>1}, where μ is a Borel probability measure on ℝ. We give a formula for the density of the absolutely continuous part of μ □t and use this formula to obtain certain regularizing properties of μ □t. We show that the number n(t) of the components in the support of μ □t is a nonincreasing function of t and give equivalent conditions so that n(t)=1 for sufficiently large t. Moreover, a measure μ so that μ □t has infinitely many components in the support for all t>1 is given.