[2] Sur un principe nouveau pour l’évaluation des fonctions holomorphes

  • Peter Duren
Part of the Contemporary Mathematicians book series (CM)


In this early paper, Schiffer applies the Schwarz lemma and the classical growth and distortion theorems of geometric function theory to deduce similar inequalities for a general analytic function \(f(z) = z + a_{2}{z}^{2} + \cdots \) in the unit disk \(\mathbb{D}\). Let Ω denote the set of values assumed by f, and let \(\widehat{\Omega }\) be the simply connected domain bounded by the outer boundary C of Ω.


Analytic Function Large Body Unit Disk Early Paper Outer Boundary 
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  1. [D]
    Peter L. Duren, Univalent Functions, Springer-Verlag, 1983.Google Scholar
  2. [G]
    G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, second edition, Izdat. “Nauka”, Moscow, 1966; English transl., American Mathematical Society, 1969.Google Scholar
  3. [R]
    Werner Rogosinski, Zum Majorantenprinzip der Funktionentheorie, Math. Z. 37 (1933), 210–236. Peter Duren MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Peter Duren
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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