Israel Journal of Mathematics

, Volume 57, Issue 3, pp 347–364 | Cite as

Generalized Grunsky coefficients and inequalities

  • Reuven Harmelin


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.


Unit Disc Explicit Formula Bergman Kernel Bernoulli Number Schwarzian Derivative 
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Copyright information

© Hebrew Univeristy 1987

Authors and Affiliations

  • Reuven Harmelin
    • 1
  1. 1.Department of MathematicsTechnion — Israel Institute of TechnologyHaifaIsrael

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