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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Invariant operators and univalent functions


Author: Reuven Harmelin
Journal: Trans. Amer. Math. Soc. 272 (1982), 721-731
MSC: Primary 30C55; Secondary 30C60
DOI: https://doi.org/10.1090/S0002-9947-1982-0662063-1
MathSciNet review: 662063
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Abstract: Necessary and sufficient conditions for univalence of meromorphic functions in certain domains in the complex plane are established in terms of some differential operators of degrees $ \ge 3$, possessing the same invariance property as the Schwarzian derivative. Those operators include the derivatives of the Schwarzian derivative and Aharonov's invariants. Conditions for the existence of quasiconformal extensions are also achieved.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0662063-1
Article copyright: © Copyright 1982 American Mathematical Society

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