## Illinois Journal of Mathematics

### Uniform approximation on Riemann surfaces by holomorphic and harmonic functions

B. Jiang

#### Abstract

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 $C(K)$.

#### Article information

Source
Illinois J. Math., Volume 47, Number 4 (2003), 1099-1113.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138093

Digital Object Identifier
doi:10.1215/ijm/1258138093

Mathematical Reviews number (MathSciNet)
MR2036992

Zentralblatt MATH identifier
1040.30020

Subjects
Primary: 30E10: Approximation in the complex domain

#### Citation

Jiang, B. Uniform approximation on Riemann surfaces by holomorphic and harmonic functions. Illinois J. Math. 47 (2003), no. 4, 1099--1113. doi:10.1215/ijm/1258138093. https://projecteuclid.org/euclid.ijm/1258138093