Alexander's projective capacity for polydisks and ellipsoids in $ℂ^N$

ArticleOriginal scientific text

Title

Authors ¹

Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

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.

ellipsoid, projective capacity, extremal function

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