Arkiv för Matematik

Transfinite diameter notions in ℂN and integrals of Vandermonde determinants

Thomas Bloom and Norman Levenberg

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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.


Bloom supported in part by an NSERC grant.

Article information

Ark. Mat., Volume 48, Number 1 (2010), 17-40.

Received: 7 February 2008
Revised: 15 March 2009
First available in Project Euclid: 31 January 2017

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2009 © Institut Mittag-Leffler


Bloom, Thomas; Levenberg, Norman. Transfinite diameter notions in ℂ N and integrals of Vandermonde determinants. Ark. Mat. 48 (2010), no. 1, 17--40. doi:10.1007/s11512-009-0101-9.

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