The General Coefficient Theorem and Certain Applications
نویسندگان
چکیده
Teichmüller was the first person to point out explicitly the connection between quadratic differentials and the solutions of certain extremal problems in Function Theory. He enunciated the principle that if a point is required to be fixed the quadratic differential will have a simple pole there, if in addition fixed values are required for the first n derivatives of competing functions the quadratic differential will have a pole of order n + 1. He was led to this principle by abstraction from the numerous results of Grötzsch and by his considerations on quasiconformal mapping. However, he never proved any general result embodying this principle. The General Coefficient Theorem provides such a result and includes as special cases virtually every result in the theory of univalent functions. We now formulate it in the following form [6; 8] , more general than that of earlier statements [ l ; 2] .
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