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Improved Versions of Forms of Plessner's Theorem

Published online by Cambridge University Press:  20 November 2018

Peter Colwell*
Affiliation:
Iowa State University, Ames, Iowa
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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
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Collingwood, E. F., A boundary theorem for Tsuji functions, Nagoya Math. J. 29 (1967), 197200.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), 277282.Google Scholar
4. Gauthier, P., The non-Plessner points for the Schwarz triangle functions, Ann. Acad. Sci. Fenn. A I 422 (1968), 16.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), 4157.Google Scholar
6. Meier, K., Über die Randwerte der meromorphen Funktionen, Math. Ann. 142 (1961), 328344.Google Scholar
7. Plessner, A.I., Über das Verhalten analytischer Funktionen am Rande Hires Definitionsbereichs, J. Reine Angew. Math. 158 (1927), 219227.Google Scholar