Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-18T09:55:29.976Z Has data issue: false hasContentIssue false
  • English
  • Français

On Strongly Normal Functions

Published online by Cambridge University Press:  20 November 2018

Huaihui Chen  and
Paul M. Gauthier
Huaihui Chen
Affiliation:
Department of Mathematics, Nanjing Normal University, NanjingJiangsu 210024, RR. CHINA, [email protected]
Paul M. Gauthier
Affiliation:
Département de Mathématiques et de Statistique, Université de Montréal, MontréalQuébec H3C 3J7, CANADA, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Loosely speaking, a function (meromorphic or harmonic) from the hyperbolic disk of the complex plane to the Riemann sphere is normal if its dilatation is bounded. We call a function strongly normal if its dilatation vanishes at the boundary. A sequential property of this class of functions is proved. Certain integral conditions, known to be sufficient for normality, are shown to be in fact sufficient for strong normality.

Keywords

30D45Normal functionsautomorphic functions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 4 , 01 December 1996 , pp. 408 - 419
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Aulaskari, R., Hayman, W. K., and Lappan, P., An integral criterion for automorphic and rotation automorphic functions, Ann. Acad. Sci. Fenn., Series A. I. Math. 15(1990), 201–224.Google Scholar
2. Aulaskari, R. and Lappan, P., On additive automorphic and rotation automorphic functions, Ark. Mat. 22(1984), 83–89.Google Scholar
3. Aulaskari, R. and Lappan, P., An integral condition for harmonic normal functions, Complex Variables 23(1993), 213—219.Google Scholar
4. Dufresnoy, J., Sur l'aire sphérique décrite par les valeurs d'une fonction mèromorphe, Bull. Sci. Math. 65(1941), 214–219.Google Scholar
5. Lappan, P., Some sequential properties of normal and non-normal functions with application to automorphic functions, Comm. Math. Univ. Sancti Pauli 12(1964), 41–57.Google Scholar
6. Lappan, P., Some results on harmonic normal functions, Math. Zeitschr. 90(1965), 155—159.Google Scholar
7. Lehto, O. and Virtanen, K. I., Boundary behaviour and normal meromorphic functions, Acta Math. 97(1957), 47–65.Google Scholar
8. Pommerenke, Ch., On normal and automorphic functions, Michigan Math. J. 21(1974), 193—202.Google Scholar
9. Schiff, J. L., Normal Families, Springer Verlag, New York, 1993.Google Scholar