Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T13:30:18.018Z Has data issue: false hasContentIssue false
  • English
  • Français

Hankel determinants and meromorphic functions

Published online by Cambridge University Press:  26 February 2010

Ch. Pommerenke
Ch. Pommerenke
Affiliation:
Technische Universitat, Berlin 12.
Get access

Extract

Let G be a plane domain with ∞ ∊ G. Let E be the compact complement of G and cap E the logarithmic capacity. We shall assume that cap E = 1 and E ⊂ {|Z| ≤ R. Then R ≥ 1, with equality if and only if E is a closed disc.

Type
Research Article
Information
Mathematika , Volume 16 , Issue 2 , December 1969 , pp. 158 - 166
Copyright
Copyright © University College London 1969

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Cantor, D. G., “Power series with integral coefficients”, Bull. Amer. Math. Soc, 69 (1963), 362–366.CrossRefGoogle Scholar
2.Edrei, A., “Sur les déterminants recurrents et les singularity d'une fonction donnee par son développement de Taylor”, Compositio Math., 7 (1939), 1–69.Google Scholar
3.Grunsky, H., “Koeffizientenbedingungen für schlicht abbildende meromorphe Funktionen”, Math. Zeit., 45 (1939), 29–61.CrossRefGoogle Scholar
4.Hadamard, J., “Essai sur l'étude des fonctions donnée par leurs développement de Taylor”, J. de Math, (4), 9 (1892), 171–215.Google Scholar
5.Pólya, G., “Über gewisse notwendige Determinantenkriterien für die Fortsetzbarkeit einer Potenzreihe”, Math. Ann., 99 (1928), 687–706.CrossRefGoogle Scholar
6.Polya, G. and Szegö, G., Aufgaben und Lehrsätze aus der Analysis, Vol. II (Berlin, 1925).Google Scholar
7.Pommerenke, Ch., “Über die Faberschen Polynome schlichter Funktionen”, Math. Zeit., 85 (1964), 197–208.CrossRefGoogle Scholar
8.Warschawski, S. E., “On differentiability at the boundary in conformal mapping”, Proc. Amer. Math. Soc, 12 (1961), 614–620.CrossRefGoogle Scholar
9.Wilson, R., “An extension of the Hadamard-Polya determinantal criteria for uniform functions”, Proc. London Math. Soc. (2), 39 (1935), 363–371.CrossRefGoogle Scholar