Hostname: page-component-7b9c58cd5d-hxdxx Total loading time: 0 Render date: 2025-03-14T22:32:28.089Z Has data issue: false hasContentIssue false
  • English
  • Français

Order of functions bounded on a spiral

Published online by Cambridge University Press:  22 January 2016

Joseph Warren
Joseph Warren*
Affiliation:
Fordham 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.

The purpose of this paper is to improve a result of Schnitzer and Seidel [6] and to continue an analogy between entire functions and the class of functions which are holomorphic and unbounded in the unit disk, but bounded on a boundary spiral. The existence of such functions was established by Valiron [7].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 51 , September 1973 , pp. 191 - 208
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

[1] Ahlfors, L., Untersuchungen zur Theorie der konformen Abbildung und der ganzen Functionen, Acta Societatis Scientiarum Fennicae, Nova Series A, vol. 1 (1930).Google Scholar
[2] Bagemihl, F., and Seidel, W., Koebe arcs and Fatou points of normal functions, Comment. Math. Helv., 36 (1961).Google Scholar
[3] Boas, R., Entire Functions, Academic Press Inc., New York, N.Y., (1954).Google Scholar
[4] Maclntyre, A., On the asymptotic paths of integral functions of finite order, Journal London Mathematical Society, vol. 10 (1935), pp. 34–39.CrossRefGoogle Scholar
[5] Phragmén, E., Lindelöf, E., Sur une extension d’un principe classique de l’Analyse et sur quelques propriétés des functions monogénes dans le voisinage d’un point singulier, Acta Mathematica, vol. 31 (1908), pp. 381–406.Google Scholar
[6] Schnitzer, F., and Seidel, W., On the modulus of unbounded holomorphic functions, Mathematische Zeitschrift, vol. 88 (1965), pp. 301–308.Google Scholar
[7] Valiron, G., Sur les singularités de certains functions holomorphes et de leurs inverses, Journal de Mathématiques pures et appliquées (9), vol. 15 (1936), pp. 432–435.Google Scholar