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Let μ⊞ν and μ⊠ν denote the free additive convolution and the free multiplicative convolution, respectively, of the Borel probability measures μ and ν. We analyze the boundary behavior of the functions Gμ⊞ν(z)=∫1z−td(μ⊞ν)(t) and ψμ⊠ν(z)=∫zt1−ztd(μ⊠ν)(t). We prove that, under certain conditions, these functions extend continuously to the boundary of their natural domains as functions with values in...
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