Uniform approximation on Riemann surfaces by holomorphic and harmonic functions
Jiang, B.
Illinois J. Math., Tome 47 (2003) no. 4, p. 1099-1113 / Harvested from Project Euclid
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Let $K$ be a compact subset of an open Riemann surface. We prove that if $L$ is a peak set for $A(K)$, then $A(K)|L=A(L).$ We also prove that if $E$ is a compact subset of $K$ with no interior such that each component of $E^c$ intersects $K^c$, then $A(K)|E$ is dense in $C(E)$. One consequence of the latter result is a characterization of the real-valued continuous functions that when adjoined to $A(K)$ generate $C(K)$.
Publié le : 2003-10-15
Classification:  30E10 
@article{1258138093,
     author = {Jiang, B.},
     title = {Uniform approximation on Riemann surfaces by holomorphic and harmonic functions},
     journal = {Illinois J. Math.},
     volume = {47},
     number = {4},
     year = {2003},
     pages = { 1099-1113},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138093}
}

Jiang, B. Uniform approximation on Riemann surfaces by holomorphic and harmonic functions. Illinois J. Math., Tome 47 (2003) no. 4, pp.  1099-1113. http://gdmltest.u-ga.fr/item/1258138093/