Transfinite diameter notions in ℂN and integrals of Vandermonde determinants

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 ( 20...

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Bibliographic Details
Published in:Arkiv för matematik 2010-04, Vol.48 (1), p.17-40
Main Authors: Bloom, Thomas, Levenberg, Norman
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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 .
ISSN:0004-2080
1871-2487
DOI:10.1007/s11512-009-0101-9