Hostname: page-component-848d4c4894-xfwgj Total loading time: 0 Render date: 2024-06-28T21:41:33.931Z Has data issue: false hasContentIssue false
  • English
  • Français

Improved Versions of Forms of Plessner's Theorem

Published online by Cambridge University Press:  20 November 2018

Peter Colwell
Peter Colwell*
Affiliation:
Iowa State University, Ames, Iowa
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.

With the aid of a theorem about the Julia points of a function meromorphic in the unit disk, this paper strengthens a theorem of K. Meier. As a consequence a stronger form of Plessner's Theorem is seen to hold which contains a theorem of E. F. Collingwood. An additional consequence is a stronger form of Meier's analogue to Plessner's Theorem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 251 - 255
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Collingwood, E. F., A boundary theorem for Tsuji functions, Nagoya Math. J. 29 (1967), 197–200.Google Scholar
2. Collingwood, E. F. and Lohwater, A. J., The theory of cluster sets (Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge, 1966).Google Scholar
3. Gauthier, P., A criterion for normalcy, Nagoya Math. J. 32 (1968), 277–282.Google Scholar
4. Gauthier, P., The non-Plessner points for the Schwarz triangle functions, Ann. Acad. Sci. Fenn. A I 422 (1968), 1–6.Google Scholar
5. Lappan, P., Some sequential properties of normal and non-normal functions with applications to automorphic functions, Comm. Math. Univ. Sancti Pauli 12 (1964), 41–57.Google Scholar
6. Meier, K., Über die Randwerte der meromorphen Funktionen, Math. Ann. 142 (1961), 328–344.Google Scholar
7. Plessner, A.I., Über das Verhalten analytischer Funktionen am Rande Hires Definitionsbereichs, J. Reine Angew. Math. 158 (1927), 219–227.Google Scholar