Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On sets of mutually disjoint univalent meromorphic functions

Author: Reuven Harmelin
Journal: Proc. Amer. Math. Soc. 86 (1982), 439-446
MSC: Primary 30C55; Secondary 30D30
MathSciNet review: 671211
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Several conditions are established for a set of meromorphic functions in a given domain $ D$, in the complete complex plane, to consist of mutually disjoint univalent functions in terms of a certain class of differential operators which are invariant under the Möbius group.

References [Enhancements On Off] (What's this?)

  • [1] D. Aharonov, A necessary and sufficient condition for univalence of a meromorphic function, Duke Math. J. 36 (1969), 599-605. MR 0249622 (40:2865)
  • [2] -, On pairs of functions and related topics, Duke Math. J. 40 (1973), 669-676. MR 0320298 (47:8837)
  • [3] D. Aharonov and M. Lavie, Disjoint meromorphic functions and nonoscillatory differential systems, Trans. Amer. Math. Soc. 187 (1974), 203-216. MR 0344472 (49:9211)
  • [4] A. F. Beardon and F. W. Gehring, Schwarzian derivative, Poincaré metrics and the kernel function, Comment. Math. Helv. 55 (1980), 50-64. MR 569245 (81c:30020)
  • [5] S. Bergman and M. M. Schiffer, Kernel functions and conformal mapping, Compositio Math. 8 (1951), 205-249. MR 0039812 (12:602c)
  • [6] J. Burbea, The Schwarzian derivative and the Poincaré metric, Pacific J. Math. 85 (1979), 345-354. MR 574922 (81g:30013)
  • [7] R. Harmelin, Invariant operators and univalent functions, Trans. Amer. Math. Soc. (to appear). MR 662063 (83k:30019)
  • [8] -, Aharonov's invariants and univalent functions, unpulished.
  • [9] -, Bergman kernel function and univalent functions, unpublished.
  • [10] -, Symmetric generating function for the derivatives of the Schwarzian derivative of univalent function, unpublished.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30C55, 30D30

Retrieve articles in all journals with MSC: 30C55, 30D30

Additional Information

Keywords: Mutually disjoint functions, univalent functions, invariants
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society