Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-15T11:06:39.086Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Results and Problems Concerning Chordal Principal Cluster Sets*

Published online by Cambridge University Press:  22 January 2016

F. Bagemihl
F. Bagemihl*
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 Γ be the unit circle and D be the open unit disk in the complex plane, and denote the Riemann sphere by Ω. By an arc at a point ζ∈Γ we mean a continuous curve such that |z(t)| < 1 for 0 ≦ t < 1 and . A terminal subarc of an arc Λ at ζ is a subarc of the form z = z (t) (t 0 ≦ t < 1), where 0 ≦ t 0<1. Suppose that f(z) is a meromorphic function in D. Then A(f) denotes the set of asymptotic values of f; and if ζ∈Γ, then C(f, ζ) means the cluster set of f at ζ and is the outer angular cluster set of f at ζ (see [13]).

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 29 , March 1967, pp. 7 - 18
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1967

Footnotes

*

Research supported by the National Science Foundation.

References

[1] Bagemihl, F., Curvilinear cluster sets of arbitrary functions, Proc. Nat. Acad. Sci. 41 (1955), 379–382.CrossRefGoogle ScholarPubMed
[2] Bagemihl, F., Characterization of the set of values approached by a meromorphic function on sequences of Jordan curves, Ann. Acad. Sci. Fennicee A I 328 (1963), 1–14.Google Scholar
[3] Bagemihl, F., Some approximation theorems for normal functions, Ann. Acad. Sci. Fennicae A I 335 (1963), 1–5.Google Scholar
[4] Bagemihl, F., Some boundary properties of normal functions bounded on nontangential arcs, Archiv der Math. 14 (1963), 399–406.Google Scholar
[5] Bagemihl, F., Piranian, G. and Young, G. S., Intersections of cluster sets, Bui. Inst. Politehn. Iasi (N. S.) 5 (1959), 29–34.Google Scholar
[6] Bagemihl, F. and Seidel, W., Spiral and other asymptotic paths, and paths of complete in détermination, of analytic and meromorphic functions, Proc. Nat. Acad. Sci. 39 (1953), 1251–1258.Google Scholar
[7] Bagemihl, F. and Seidel, W., Some boundary properties of analytic functions, Math. Zeitschr. 61 (1954), 186–199.Google Scholar
[8] Bagemihl, F. and Seidel, W., Some remarks on boundary behavior of analytic and meromorphic functions, Nagoya Math. J. 9 (1955), 79–85.CrossRefGoogle Scholar
[9] Bieberbacb, L., Lehrbuch der Funktionentheorie (2d ed.) vol. 2, Leipzig, 1931.Google Scholar
[10] wood, E. F. Colling, On sets of maximum indétermination of analytic functions, Math. Zeitschr. 67 (1957), 377–396.Google Scholar
[11] Gross, W., Über die Singularitäten analytischer Funktionen, Mh. Math. Phys. 29 (1918), 3–47.Google Scholar
[12] Meier, K., Über die Randwerte der meromorphen Funktionen, Math. Ann. 142 (1961), 328–344.Google Scholar
[13] Noshiro, K., Cluster sets, Berlin, 1960.CrossRefGoogle Scholar
[14] Rudin, W., Principles of mathematical analysis, New York, 1953.Google Scholar
[15] Tsuji, M., Potential theory in modern function theory, Tokyo, 1959.Google Scholar