Abstract
Several properties of a certain series of differential operators which are invariant under the Möbius group (Aharonov invariants) are proved, and in terms of this series new conditions for univalence and quasiconformal extendability of meromorphic functions are established.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Aharonov,A necessary and sufficient condition for univalence of a meromorphic function, Duke Math. J.36 (1969), 599–604.
L. V. Ahlfors and L. Bers,Riemann's mapping theorem for variable metrics, Ann. of Math.72 (1960), 385–404.
L. Comtet,Advanced Combinatorics. The Art of Finite and Infinite Expansions, Reidel, Dordrecht and Boston, Mass., 1974.
R. Harmelin,Invariant operators and univalent functions, Trans. Am. Math. Soc., to appear.
R. Harmelin,Affine and projective invariants, generalized Grunsky coefficients and Bernoulli numbers, unpublished.
E. Jabotinsky,Representation of functions by matrices, application to Faber polynomials, Proc. Am. Math. Soc.4 (1953), 546–553.
O. Lehto,Schlict functions with a quasiconformal extension, Ann. Acad. Sci. Fenn. A.I.500 (1971), 1–10.
O. Lehto,Conformal mappings and Teichmüller spaces, Lectures at the Technion, Haifa, Israel, April–May, 1973.
P. G. Todorov,Explicit formulas for the coefficients of Faber polynomials with respect to univalent functions of the class Σ Proc. Am. Math. Soc.82 (1981), 431–438.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Harmelin, R. Aharonov invariants and univalent functions. Israel J. Math. 43, 244–254 (1982). https://doi.org/10.1007/BF02761945
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02761945