The homogeneous transfinite diameter of a compact subset of $ℂ^N$

Mieczysław Jędrzejowski

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Displaying similar documents to “The homogeneous transfinite diameter of a compact subset of $ℂ^{N}$ ”

Alexander’s projective capacity for polydisks and ellipsoids in $ℂ^{N}$

Mieczysław Jędrzejowski (1995)

Annales Polonici Mathematici

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Alexander’s projective capacity for the polydisk and the ellipsoid in $ℂ^{N}$ is computed. Sharper versions of two inequalities concerning this capacity and some other capacities in $ℂ^{N}$ are given. A sequence of orthogonal polynomials with respect to an appropriately defined measure supported on a compact subset K in $ℂ^{N}$ is proved to have an asymptotic behaviour in $ℂ^{N}$ similar to that of the Siciak homogeneous extremal function associated with K.

On the multivariate transfinite diameter

Thomas Bloom, Jean-Paul Calvi (1999)

Annales Polonici Mathematici

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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.

Homogeneous extremal function for a ball in ℝ²

Mirosław Baran (1999)

Annales Polonici Mathematici

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We point out relations between Siciak’s homogeneous extremal function $Ψ_{B}$ and the Cauchy-Poisson transform in case $B$ is a ball in ℝ². In particular, we find effective formulas for $Ψ_{B}$ for an important class of balls. These formulas imply that, in general, $Ψ_{B}$ is not a norm in ℂ².