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Homogeneous extremal function for a ball in ℝ²

Mirosław Baran (1999)

Annales Polonici Mathematici

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.

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