Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-17T03:13:39.872Z Has data issue: false hasContentIssue false

A Boundary Theorem for Tsuji Functions

Published online by Cambridge University Press:  22 January 2016

E. F. Collingwood*
Affiliation:
Lilburn Tower, Alnwick, England
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 denote the unit disc | z | <1, C the unit circle | z | = 1 and Cr the circle | z| = r. Corresponding to any function w(z) meromorphic in D we denote by w*(z) the spherical derivative

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1967

References

[1] Tsuji, M. A theorem on the boundary behaviour of a meromorphic function in | z | < 1. Comment. Math. Univ. St. Paul, 8 (1960), 5355.Google Scholar
[2] Bagemihl, F. Curvilinear cluster sets of arbitrary functions. Proc. Nat. Acad. Sci. U.S.A., 41 (1955), 379382.CrossRefGoogle ScholarPubMed
[3] Collingwood, E. F. and Piranian, G. Tsuji functions with segments of Julia. Math. Zeitschr., 84 (1964), 246253.CrossRefGoogle Scholar
[4] Collingwood, E. F. and Lohwater, A. J. The theory of cluster sets, Cambridge, 1966.CrossRefGoogle Scholar
[5] Privalov, I. I. Randeigenschaften analytischer Funktionen, Berlin, 1956.Google Scholar
[6] Meier, , Kurt Uber die Randwerte der meromorphen Funktionen. Math. Annalen., 142 (1961), 328344.Google Scholar