Transfinite diameter notions in ℂ^{$N$}and integrals of Vandermonde determinants

Thomas Bloom University of Toronto, Toronto, Ontario, Canada Norman Levenberg Indiana University, Bloomington, IN, U.S.A.

TBD mathscidoc:1701.333157

Arkiv for Matematik, 48, (1), 17-40, 2008.2
We provide a general framework and indicate relations between the notions of transfinite diameter, homogeneous transfinite diameter, and weighted transfinite diameter for sets in ℂ^{$N$}. An ingredient is a formula of Rumely (A Robin formula for the Fekete–Leja transfinite diameter,$Math. Ann.$$337$(2007), 729–738) which relates the Robin function and the transfinite diameter of a compact set. We also prove limiting formulas for integrals of generalized Vandermonde determinants with varying weights for a general class of compact sets and measures in ℂ^{$N$}. Our results extend to certain weights and measures defined on cones in ℝ^{$N$}.
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@inproceedings{thomas2008transfinite,
  title={Transfinite diameter notions in ℂ^{$N$}and integrals of Vandermonde determinants},
  author={Thomas Bloom, and Norman Levenberg},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203625897541966},
  booktitle={Arkiv for Matematik},
  volume={48},
  number={1},
  pages={17-40},
  year={2008},
}
Thomas Bloom, and Norman Levenberg. Transfinite diameter notions in ℂ^{$N$}and integrals of Vandermonde determinants. 2008. Vol. 48. In Arkiv for Matematik. pp.17-40. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203625897541966.
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