Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 851-874

p-TRANSFINITE DIAMETER AND p-CHEBYSHEV CONSTANT IN LOCALLY COMPACT SPACES

Ágota P. Horváth

Budapest University of Technology and Economics, Department of Analysis
Muegyetem rakpart 3, H-1521 Budapest, Hungary; g.horvath.agota 'at' renyi.mta.hu

Abstract. We extend the notion of transfinite diameter and Chebyshev constant to p-potential theory in locally compact spaces and study their relations. As in the classical case, it turns out that provided that the kernel satisfies a certain condition, for any compact sets the energy, the Chebyshev constant and the transfinite diameter are coincide. The investigations follow the linear method developed by e.g. Choquet, Fuglede, Ohtsuka, Farkas and Nagy. Taking into consideration the significance of finite sets of the minimal and almost minimal energy, we examine Fekete and greedy energy sets as well.

2010 Mathematics Subject Classification: Primary 31C15, 31C45.

Key words: p-energy, p-transfinite diameter, p-Chebyshev constant, greedy energy points.

Reference to this article: Á.P. Horváth: p-Transfinite diameter and p-Chebyshev constant in locally compact spaces. Ann. Acad. Sci. Fenn. Math. 40 (2015), 851-874.

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doi:10.5186/aasfm.2015.4047