Abstract
We prove that for an arbitrary positive continuous function Φ on the complex plane ℂ there exists an injective disc algebra function φ and n ∈ ℕ such that ξ ↦ φ(ξ n ) solves Beurling’s boundary differential relation |f′(ξ)| = Φ(f(ξ)) on ∂Δ. Moreover, if the growth of Φ is sublinear, the existence of univalent solutions of Beurling’s boundary differential relation is shown.
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