Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T23:39:41.158Z Has data issue: false hasContentIssue false

Continua Which are Curvilinear Cluster Sets

Published online by Cambridge University Press:  22 January 2016

Peter Lappan*
Affiliation:
Michigan State 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.

Let D be the unit disk | z | < 1 and let f be a complex-valued function continuous in D. The cluster set C(f, e) of f at e is defined by

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1969

References

[1] Bagemihl, F. and Seidel, W., Some boundary properties of analytic functions, Math. Z. 61 (1954), 186199.Google Scholar
[2] Bagemihl, F. and Seidel, W., Functions of bounded characteristic with prescribed ambiguous points, Michigan Math, J. 3 (195556), 7781.Google Scholar
[3] Collingwood, E.F. and Lohwater, A.J., The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, Cambridge University Press, 1966.Google Scholar