Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-08T16:14:59.250Z Has data issue: false hasContentIssue false

Extremal Problems for Schlicht Functions in the Exterior of the Unit Circle

Published online by Cambridge University Press:  20 November 2018

E. Netanyahu*
Affiliation:
Technion, Israel Institute of Technology, Haifa
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 Σ represent the class of functions

(1)

which are schlicht and regular, except for the pole at infinity, in |z| > 1. Further let Σ-1 be the class of inverse functions of Σ which at w = ∞ have the expansion

(2)

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Garabedian, P. R. and Schiffer, M., A coefficient inequality for schlicht functions, Ann. of Math., 61 (1955), 116–36.Google Scholar
2. Löwner, K., Untersuchungen ùber schlichte konforme Abbildungen des Einheitskreises, Math. Ann., 89 (1923), 103–21.Google Scholar
3. Netanyahu, E., The coefficients problem for schlicht functions in the exterior of the unit circle, Technical Report No. 39 (1954), Dept. of Math., Stanford University.Google Scholar
4. Royster, W. C., Extremal problems for functions starlike in the exterior of the unit circle, Can J. Math., 14 (1962), 540–51.Google Scholar
5. Schaeffer, A. C. and Spencer, D. C., Coefficient regions for schlicht functions (New York, 1950).Google Scholar
6. Schiffer, M., A method of variation within the family of simple functions, Proc. London Math. Soc, 14 (1938), 432-49.Google Scholar
7. Schiffer, M., Variation of the Green function and theory of the p-valued functions, Amer. J. Math., 65 (1943), 341–60.Google Scholar
8. Springer, G., The coefficient problem for schlicht mappings of the exterior of the unit circle, Trans. Amer. Math. Soc, 70 (1951), 421–50.Google Scholar