The domain of univalence of certain families of rational functions
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- by A. W. Goodman PDF
- Proc. Amer. Math. Soc. 66 (1977), 85-90 Request permission
Abstract:
The Čakalov-Distler Theorem gives the domain of univalence for the family of all rational functions for which all the poles are simple, all the poles lie in a prescribed convex set, and all have positive residue. Here we extend this theorem to allow simple poles with negative residues. We include several open problems.References
- Lubomir Tchakaloff, Sur une classe de fonctions analytiques univalentes, C. R. Acad. Sci. Paris 242 (1956), 437–439 (French). MR 75300
- L. Čakalov, Sur les domaines d’univalence de certaines classes de fonctions analytiques, Bŭlgar. Akad. Nauk Izv. Mat. Inst. 4 (1960), no. 2, 43–55 (1960) (Bulgarian, with Russian and French summaries). MR 0123700
- Raymond J. Distler, The domain of univalence of certain classes of meromorphic functions, Proc. Amer. Math. Soc. 15 (1964), 923–928. MR 167610, DOI 10.1090/S0002-9939-1964-0167610-9 S. Lameier, On domains of univalence of certain meromorphic functions, Master’s Thesis, University of Cincinnati, Cincinnati, Ohio.
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 85-90
- MSC: Primary 30A32
- DOI: https://doi.org/10.1090/S0002-9939-1977-0584957-1
- MathSciNet review: 0584957