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31-XX Potential theory
31Cxx Other generalizations
31C15 Potentials and capacities

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Harmonie Continuation and Removable Singularities in the Axiomatic Potential Theory.

Ivan Netuka, Jiri Vesely (1978)

Mathematische Annalen

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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