Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-16T00:40:35.150Z Has data issue: false hasContentIssue false
  • English
  • Français

Normal Functions and Non-Tangential Boundary Arcs

Published online by Cambridge University Press:  20 November 2018

P. Lappan  and
D. C. Rung
P. Lappan
Affiliation:
Lehigh University and Pennsylvania State University
D. C. Rung
Affiliation:
Lehigh University and Pennsylvania State University
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 and C denote respectively the open unit disk and the unit circle in the complex plane. Further, γ = z(t), 0 ⩽ t ⩽ 1, will denote a simple continuous arc lying in D except for Ƭ = z(l) ∈ C, and we shall say that γ is a boundary arc at Ƭ.

We use extensively the notions of non-Euclidean hyperbolic geometry in D and employ the usual metric

where a and b are elements of D. For a ∈ D and r > 0 let

For details we refer the reader to (4).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 256 - 264
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Bagemihl, F., Some approximation theorems for normal functions, Ann. Acad. Sci. Fenn. Ser. A, I (1963), 335.Google Scholar
2. Bagemihl, F. and Seidel, W., Spiral and other asymptotic paths, and paths of complete indetermination, of analytic and meromorphic functions, Proc. Nat. Acad. Sci. U.S.A., 39 (1953), 1251–1258.Google Scholar
3. Bagemihl, F. and Seidel, W., Köebe arcs and Fatou points of normal functions, Comment. Math. Helvt., 36 (1961), 9–18.Google Scholar
4. Behnke, H. and Sommer, F., Theorie der analytischen Funktionen einer komplexen Veränderlichen (Berlin, 1955).Google Scholar
5. Cargo, G. T., Normal functions, the Montel property, and interpolation in H∞ , Michigan Math. J., 10 (1963), 141–146.Google Scholar
6. Lehto, O. and Virtanen, K. I., Boundary behavior and normal meromorphic functions, Acta Math., 97 (1957), 47–64.Google Scholar
7. Noshiro, K., Cluster sets (Berlin, 1960).Google Scholar
8. Rung, D. C., Boundary behavior of normal functions defined in the unit disk, Michigan Math. J., 10 (1963), 43–51.Google Scholar
9. Hurwitz, A. and Courant, R., Vorlesungen iiber allgemeine Funktionentheorie und elliptische Funktionen (Berlin-Göttingen-Heidelberg-New York: vierte Auflage, 1964).Google Scholar