Functions in H ■ //(D) are sense-preserving of the form f = h ■ g where h and g are in H(D). Such functions are solutions of an elliptic nonlinear P.D.E. that is studied in detail especially for its univalent solutions.
Let H(U) be the linear space of holomorphic functions defined on the unit disk U endowed with the topology of normal (locally uniform) convergence. For a subset E ⊂ H(U) we denote by Ē the closure of E with respect to the above topology. The topological dual space of H(U) is denoted by H′(U).Let D, 0 ∊ D, be a simply connected domain in C. The unique univalent conformal mapping ϕ from U onto D, normalized by ϕ(0) = 0 and ϕ′(0) > 0 will be called “the Riemann Mapping onto D”. Let S be the set of all normalized univalent functions
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