Publishing house / Journals and Serials / Annales Polonici Mathematici / All issues

Abstract

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.