Generalized dimension compression under mappings of exponentially integrable distortion

Aleksandra Zapadinskaya

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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.