Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-01T06:47:20.425Z Has data issue: false hasContentIssue false

Non-Essential Cluster Values and Normal Functions

Published online by Cambridge University Press:  22 January 2016

C. L. Belna*
Affiliation:
Wright State University, Dayton, Ohio 45431
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.

We consider continuous functions f which map the open unit disk D into the Riemann sphere W. For a point ζ on the unit circle C, we say that χ is a chord at ζ if χ is a chord of C having one endpoint at ζ and that Δ is a Stolz angle at ζ if Δ is a Stolz angle with vertex ζ. Suppose S denotes either a chord at ζ, a Stolz angle at ζ, or D.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

[1] Bagemihl, P. and Seidel, W., Some boundary properties of analytic functions, Math. Z., 61 (1954), 186199.Google Scholar
[2] Goffman, Casper and Sledd, W. T., Essential Cluster Sets, J. London Math. Soc, (2), 1 (1969), 295302.Google Scholar
[3] Lappan, Peter, Some sequential properties of normal and non-normal functions with applications to automorphic functions, Comm. Math. Univ. Sancti Pauli, 12 (1964), 4157.Google Scholar
[4] Lappan, Peter, Some results on harmonic normal functions, Math. Z., 90 (1965), 155159.Google Scholar
[5] Littlewood, J. E., Mathematical Notes (4): On a theorem of Fatou, London Math. J., 2 (1947), 172176.Google Scholar
[6] Noshiro, K., Cluster sets, Berlin, 1960.CrossRefGoogle Scholar
[7] Rung, D. C., Behavior of holomorphic functions in the unit disk on arcs of positive hperbolyic diameter, J. Math. Kyoto Univ., 8-3 (1968), 417464.Google Scholar