The paper explicitly parametrizes all free additive Lévy functions of the second kind (for initial law δ0) as φ = ψ∘Φ, where Ψ is a conformal map whose image contains the upper half-plane and ψ is a Nevanlinna function.
Pommerenke , Univalent functions
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Nonlinear free L\'evy-Khinchine formula and conformal mapping
The paper explicitly parametrizes all free additive Lévy functions of the second kind (for initial law δ0) as φ = ψ∘Φ, where Ψ is a conformal map whose image contains the upper half-plane and ψ is a Nevanlinna function.