Generalized Grunsky coefficients and inequalities
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The generalized Grunsky coefficients are defined in this paper for all locally univalent meromorphic functions in any domain in the complete complex plane. Various explicit formulas for these coefficients are established. Necessary conditions for univalence are obtained in arbitrary domains and in the unit disc in particular. The first one generalizes Grunsky inequalities and the second one is an extension of the Nehari-Schwarzian derivative condition.
KeywordsUnit Disc Explicit Formula Bergman Kernel Bernoulli Number Schwarzian Derivative
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