## Invariant operators and univalent functions

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- by Reuven Harmelin PDF
- Trans. Amer. Math. Soc.
**272**(1982), 721-731 Request permission

## 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.## References

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## Additional Information

- © Copyright 1982 American Mathematical Society
- 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