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On the distribution of Fekete points II

Part of: Two-dimensional theory

Published online by Cambridge University Press:  26 February 2010

T. Kövari
T. Kövari
Affiliation:
Department of Mathematics, Imperial College, London
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Extract

In a paper of the same title [3] Ch. Pommerenke and the author proved several results concerning the distances of Fekete points. In the present paper I will show that the same methods can be adapted to give an answer to a problem which we could not solve at the time.

Let E be a continuum and n ≥ 4 a given positive integer. A system of points z1, …, zn ∈ E that maximizes

is called a system of Fekete points. Such a system may not be unique.

MSC classification

Secondary: 31A15: Potentials and capacity, harmonic measure, extremal length

Information

Type
Research Article
Information
Mathematika , Volume 18 , Issue 1 , June 1971 , pp. 40 - 49
Copyright
Copyright © University College London 1971

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References

1.Goluzin, G. M., Geometrische Funktionentheorie (Berlin, 1957).Google Scholar
2.Kövari, T. and Pommerenke, Ch., “On Faber polynomials and Faber Expansions”, Math. Zeit., 99 (1967), 193–206.CrossRefGoogle Scholar
3.Kövari, T. and Pommerenke, Ch., “On the distribution of Fekete points”, Mathematika, 15 (1968), 70–75.CrossRefGoogle Scholar
4.Paatero, V.: “Über die konforme Abbildung von Gebieten deren Ränder von beschränkter Drehung sind”, Ann. Acad. Sci. Fenn., Ser. A., 33 (1931), 1–77.Google Scholar
5.Pommerenke, Ch., “Konforme Abbildung und Fekete-Punkte”, Math. Zeit., 89 (1965), 422–438.CrossRefGoogle Scholar