Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T13:52:35.220Z Has data issue: false hasContentIssue false

Boundary behaviour of meromorphic functions along Green's lines

Published online by Cambridge University Press:  09 April 2009

Mikio Niimura
Affiliation:
Department of Mathematics, Shibaura Institute of Technology, 3-9-15, Shibaura, Minato-ku Tokyo, Japan
Rights & Permissions [Opens in a new window]

Abstract

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.

In this note we study the boundary behavior of meromorphic functions in bounded plane regions along Green's lines. As applications we obtatin extensions of Lohwater's theorems and Seidel's theorems concerning radial cluster sets.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1981

References

Alexandroff, P. and Hopf, H. (1935), Topologie (Springer-Verlag, Berlin).Google Scholar
Arsove, M. G. and Johnson, G. Jr (1970), ‘A conformal mapping technique for infinitely connected regions’, Mem. Amer. Math. Soc. 91, 156.Google Scholar
Collingwood, E. F. and Lohwater, A. J. (1966), The theory of cluster sets (Cambridge University Press).CrossRefGoogle Scholar
Heins, M. (1955), ‘On the Lindelöf principle’, Ann. of Math. 61, 440473.CrossRefGoogle Scholar
Lohwater, A. J. (1960), ‘On the theorems of Gross and Iversen’, J. Analyse Math. 7, 209221.CrossRefGoogle Scholar
Nagasaka, Y. (1975), ‘Notes on Green's lines’, Hokkaido Math. J. 4, 5358.CrossRefGoogle Scholar
Nagasaka, Y. (1978), ‘Cluster sets on Riemann surfaces’, Hokkaido Math. J. 7, 169177.CrossRefGoogle Scholar
Niimura, M. (1977), ‘Cluster sets on open Riemann surfaces’, Proc. Amer. Math. Soc. 66, 4648.CrossRefGoogle Scholar
Niimura, M. (1979), ‘On boundary cluster sets’, J. Reine Angew. Math. 307/308, 130133.Google Scholar
Sario, L. and Nakai, M. (1970), Classification theory of Riemann surfaces (Springer-Verlag, Berlin-Heidelberg-New York).CrossRefGoogle Scholar
Seidel, W. (1934), ‘On the distribution of values of bounded analytic functions’, Trans. Amer. Math. Soc. 36, 201226.CrossRefGoogle Scholar