Abstract
We provide a general framework and indicate relations between the notions of transfinite diameter, homogeneous transfinite diameter, and weighted transfinite diameter for sets in ℂN. 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 ℂN. Our results extend to certain weights and measures defined on cones in ℝN.
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Bloom supported in part by an NSERC grant.
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Bloom, T., Levenberg, N. Transfinite diameter notions in ℂN and integrals of Vandermonde determinants. Ark Mat 48, 17–40 (2010). https://doi.org/10.1007/s11512-009-0101-9
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DOI: https://doi.org/10.1007/s11512-009-0101-9