Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-13T02:47:23.783Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Asymptotic Behavior of Functions Harmonic in a Disc

Published online by Cambridge University Press:  22 January 2016

J. E. Mcmillan
J. E. Mcmillan*
Affiliation:
University of Wisconsin-Milwaukee
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 open unit disc, and let C be the unit circle in the complex plane. Let f be a (real-valued) function that is harmonic in D. A simple continuous curve β: z(t) (0≦t<1) contained in D such that |z(t)|→1 as t→1 is a boundary path with end (the bar denotes closure).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 28 , October 1966 , pp. 187 - 191
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Bagemihl, F. and Seidel, W.: Koebe arcs and Fatou points of normal functions, Comment. Math. Helv., 36 (1961), 9–18.CrossRefGoogle Scholar
[2] MacLane, G. R.: Asymptotic values of holomorphic functions, Rice Univ. Studies, 49 (1963), 1–83.Google Scholar
[3] McMillan, J. E.: Asymptotic values of functions holomorphic in the unit disc, Michigan Math. J., 12 (1965), 141–154.CrossRefGoogle Scholar
[4] McMillan, J. E.: On local asymptotic properties, the asymptotic value sets, and ambiguous properties of functions meromorphic in the open unit disc, Ann. Acad. Sci. Fenn., A. I., 384 (1965), 1–12.Google Scholar
[5] McMillan, J. E.: Boundary properties of functions continuous in a disc, Michigan Math. J. (to appear).Google Scholar
[6] Noshiro, K.: Cluster sets, Berlin-Göttingen-Heidelberg, 1960.CrossRefGoogle Scholar