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Harmonic and superharmonic functions on compact sets. (English) Zbl 0545.31009
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 J. Bliedtner and 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.

##### MSC:
 31C05 Harmonic, subharmonic, superharmonic functions on other spaces 41A30 Approximation by other special function classes 31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions 31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
##### Keywords:
uniform approximation; compact subset; harmonic