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On the Derivatives of the Schwarzian Derivative of a Univalent Function and their Symmetric Generating Function
Author(s) -
Harmelin Reuven
Publication year - 1983
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-27.3.489
Subject(s) - schwarzian derivative , meromorphic function , bounded function , mathematics , pure mathematics , analytic function , univalent function , complex plane , mathematical analysis , function (biology) , norm (philosophy) , domain (mathematical analysis) , invariant (physics) , derivative (finance) , unit disk , mathematical physics , evolutionary biology , political science , law , economics , biology , financial economics
For every analytic function in a domain D in the complete complex plane, bounded in a certain norm, a symmetric generating function for the series of its derivatives is constructed, bounded in another norm. New conditions are deduced for univalence and quasiconformal extendability of a meromorphic function in D in terms of the series of the derivatives of the Schwarzian derivative. In particular an inequality satisfied by Grunsky coefficients of univalent functions in the unit disc is derived.