Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-17T15:22:08.730Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Remarks on Angular Derivatives and Julia's Lemma

Published online by Cambridge University Press:  20 November 2018

H. L. Jackson
H. L. Jackson*
Affiliation:
McMaster 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 w = f(z) be holomorphic on the unit disk D = { z: | z | < 1}, with the additional restrictions that | f ( z ) | < l and , where denotes the (outer) angular limit of f (z) at z = 1. Let us now define and then focus our attention on the behaviour of g(z) in an arbitrary angular neighbourhood of z = 1. Whenever exists, this limit is commonly referred to as the angular derivative of f(z) at z = 1.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 2 , June 1966 , pp. 233 - 241
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Bieberbach, L., Lehrbuch der Funktionentheorie, Vol II, Chelsea, New York, 1945.Google Scholar
2. Brelot, M., Sur le principe des singularités positives et la topologie de R. S. Martin, Annales Univ. Grenoble, Math. Phys., 23 (1948), 113-138.Google Scholar
3. Brelot, M. and Doob, J. L., Limites angulaires et limites fines, Annales de l'institut Fourier de l'univ. Grenoble, 13 (1963), Fasc. II, 395-415.Google Scholar
4. Carathéodory, C., Theory of Functions, Vol. II, Chelsea, New York, 1954.Google Scholar
5. Dinghas, A., Vorlesungen űber Funktionentheorie. Springer, Berlin, 1961.Google Scholar
6. Gattengo, C. and Ostrowski, A., Mém. des Sciences Math. Fasc. CIX. Gauthier-Villars, Paris, 1949.Google Scholar
7. Nairn, L., Sur le röle de la frontieŕe de R. S. Martin dans la théorie du potentiel, Thesis, Paris, 1957.Google Scholar
8. Parreau, M., Sur les moyennes des fonctions harmoniques et analytiques, Annales de l'inst. Fourier de l'univ. Grenoble, 3 (1951), 103-197.Google Scholar
9. Tsuji, M., Potential theory in modern function theory. Maruzen, Tokyo, 1959.Google Scholar