Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T18:13:41.418Z Has data issue: false hasContentIssue false
  • English
  • Français

Spiral Asymptotic Values of Functions Meromorphic in the Unit Disk

Published online by Cambridge University Press:  22 January 2016

J.L. Stebbins
J.L. Stebbins*
Affiliation:
Wayne State University and The University of Wisconsin-Milwaukee
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.

This paper contains part of the author’s Ph.D. dissertation directed by Frederick Bagemihl at Wayne State University. The research was supported by a grant from the Michigan Institute of Science and Technology.

Alice Roth has made an extensive study of entire meromorphic functions with prescribed behavior along half rays emanating from the origin (6). The question arose whether analogous results could be found for functions meromorphic in the unit disk with the same behavior prescribed along an exhaustive class of spirals emanating from the origin. In this paper, I present a class of spirals which satisfactorily fills this role. However, I make no claim to the effect that only this class will suffice.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 30 , August 1967 , pp. 247 - 262
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Bagemihl, F. and Seidel, W., Some boundary properties of analytic functions. Math. Zeit. 61, 186–199 (1954).CrossRefGoogle Scholar
[2] Bohr, H., Über ganze transzendente Funktionen, die auf jeder durch den Nullpunkt gehenden Geraden beschrànkt sind. Opuse. Math. A. Wiman Dedicata (1930).Google Scholar
[3] Carathéodory, C., Über die Begrenzung einfach zusammenhängender Gebiete. Math. Annalen 73, 323–370 (1913).CrossRefGoogle Scholar
[4] Lehto, O. and Virtanen, K.I., Boundary behaviour and normal meromorphic functions. Acta Math. 97, 47–65 (1957).CrossRefGoogle Scholar
[5] Noshiro, K., Cluster Sets. Springer-Verlag, Berlin, 1960.CrossRefGoogle Scholar
[6] Roth, A., Approximationseigenschaften und Strahlengrenzwerte meromorpher und ganzer Funktionen. Comment. Math. Helvet. 11, 77–125 (1938).CrossRefGoogle Scholar
[7] Study, E., Vorlesungen über ausgewählte Gegenstände der Geometrie, Zweites Heft, Konforme Abbildung einfachzusammenhängender Bereiche. Leipzig and Berlin, 1913.Google Scholar
[8] Walsh, J.L., Interpolation and Approximation by Rational Functions in the Complex Plane. Amer. Math. Soc. Colloquium Publications. 20, Third Edition, 1960.Google Scholar