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ArticleOriginal scientific text

Title

On the multivariate transfinite diameter

Authors 1, 2

Affiliations

  1. Department of Mathematics, University of Toronto, M5S 3G3, Toronto, Ontario, Canada
  2. Laboratoire de Mathématiques E. Picard, UFR MIG, Université Paul Sabatier, 31062 Toulouse Cedex, France

Abstract

We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.

Keywords

ENG
Robin's functions, extremal plurisubharmonic functions, minimal polynomials, multivariate transfinite diameter, Chebyshev polynomials

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Annales Polonici Mathematici
1999/72/3
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Pages:
285-305
Main language of publication
English
Received
1999-06-25
Accepted
1999-10-11
Published
1999
Exact and natural sciences