Transfinite diameter, Chebyshev constant and energy on locally compact spaces
Farkas, Balint ; Nagy, Bela
arXiv, 0704.0859 / Harvested from arXiv
Text on arXiv
We study the relationship between transfinite diameter, Chebyshev constant and Wiener energy in the abstract linear potential analytic setting pioneered by Choquet, Fuglede and Ohtsuka. It turns out that, whenever the potential theoretic kernel has the maximum principle, then all these quantities are equal for all compact sets. For continuous kernels even the converse statement is true: if the Chebyshev constant of any compact set coincides with its transfinite diameter, the kernel must satisfy the maximum principle. An abundance of examples is provided to show the sharpness of the results.
Publié le : 2007-04-06
Classification:  Mathematics - Classical Analysis and ODEs,  31C15,  28A12, 54D45 
@article{0704.0859,
     author = {Farkas, Balint and Nagy, Bela},
     title = {Transfinite diameter, Chebyshev constant and energy on locally compact
  spaces},
     journal = {arXiv},
     volume = {2007},
     number = {0},
     year = {2007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0704.0859}
}

Farkas, Balint; Nagy, Bela. Transfinite diameter, Chebyshev constant and energy on locally compact
  spaces. arXiv, Tome 2007 (2007) no. 0, . http://gdmltest.u-ga.fr/item/0704.0859/