Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T23:44:19.194Z Has data issue: false hasContentIssue false
  • English
  • Français

Normal Light Interior Functions Defined in the Unit Disk

Published online by Cambridge University Press:  22 January 2016

J.H. Mathews
J.H. Mathews*
Affiliation:
Michigan State University and California State College at Fullerton
Rights & Permissions [Opens in a new window]

Extract

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.

Let D be the unit disk, C the unit circle, and f a continuous function from D into the Riemann sphere W. We say that f is normal if f is uniformly continuous with respect to the non-Euclidean hyperbolic metric in D and the chordal metric in W.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 39 , August 1970 , pp. 149 - 155
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Ahlfors, L. and Sario, L., Riemann Surfaces, Princeton Univ. Press, Princeton, New Jersey, 1965.Google Scholar
[2] Bagemihl, F. and Seidel, W., Koebe Arcs and Fatou Points of Normal Functions, Comment. Math. Helv. 36 (1961), 9–18.Google Scholar
[3] Carathéodory, C., Theory of Functions of a Complex Variable, Vol. I, 2nd ed., Chelsea, New York, 1964.Google Scholar
[4] Church, P., Extensions of Stoïlow’s Theorem, J. London Math. Soc. 37 (1962), 86–89.Google Scholar
[5] Hersch, J. and Pfluger, A., Généralisation du lemme de Schwarz et du principe de la mesure harmonique pour les fonctions pseudo-analytiques, C.R. Acad. Sci. Paris 234 (1952), 43–45.Google Scholar
[6] Hille, E., Analytic Function Theory, Vol. II, Ginn, New York, 1962.Google Scholar
[7] Lappan, P., Some Results on Harmonic Normal Functions, Math. Z. 90 (1965), 155–159.Google Scholar
[8] Lehto, O. and Virtanen, K., Boundary Behavior and Normal Meromorphic Functions, Acta Math. 97 (1957), 47–65.CrossRefGoogle Scholar
[9] Mori, A., On Quasi-Conformality and Pseudo-Analyticity, Trans. Amer. Math. Soc. 84 (1957), 56–77.Google Scholar
[10] Noshiro, K., Contributions to the Theory of Meromorphic Functions in the Unit-Circle, J. Fac. Sci. Hokkaido Univ. 7 (1939), 149–159.Google Scholar
[11] Väisälä, J., On Normal Quasiconformal Functions, Ann. Acad. Sci. Fenn. Ser. AI, no. 266 (1959), 33 pp.Google Scholar