Harmonic and superharmonic functions on compact sets (Q797726)

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scientific article; zbMATH DE number 3867703
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Harmonic and superharmonic functions on compact sets
scientific article; zbMATH DE number 3867703

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    Harmonic and superharmonic functions on compact sets (English)
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    1985
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    \textit{T. W. Gamelin} [Ill. J. Math. 26, 353-357 (1982; Zbl 0466.31004)] gave necessary and sufficient conditions which ensure that every continuous function on a compact subset K of \({\mathbb{R}}^ 2\), harmonic on the interior of K, can be approximated uniformly on K by functions harmonic in a neighborhood of K. Using results obtained by \textit{J. Bliedtner} and \textit{W. Hansen} [Invent. Math. 29, 83-110 (1975; Zbl 0308.31011), ibid. 46, 255-275 (1978; Zbl 0363.31009)] a stronger version of the same result is proved for arbitrary harmonic spaces.
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    uniform approximation
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    compact subset
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    harmonic
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