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Characteristic properties of Nehari functions

Let N be the set of all meromorphic functions f defined in the unit disc D that satisfy Nehari’s univalence criterion (1 − |z|)|Sf(z)| ≤ 2. In this paper we investigate certain properties of the class N . We obtain sharp estimates for the spherical distortion, and also a two-point distortion theorem that actually characterizes the set N . Finally, we study some aspects of the boundary behavior of Nehari functions, and obtain results that indicate how such maps can fail to map D onto a quasidisc.