## Illinois Journal of Mathematics

### Criteria for approximation by harmonic functions

T. W. Gamelin

#### Abstract

In [1], P. R. Ahern gives “geometric” conditions which ensure that every continuous function on $K$, harmonic in the interior of $\mathrm{K}$, can be approximated uniformly on $K$ by functions harmonic in a neighborhood of $K$. Here we observe that Ahern's conditions can be sharpened to yield necessary and sufficient conditions for such approximation to obtain. The proof depends on a simple characterization of stable boundary points, which facilitates the evaluation of certain logarithmic potentials.

#### Article information

Source
Illinois J. Math., Volume 26, Issue 2 (1982), 353-357.

Dates
First available in Project Euclid: 20 October 2009

https://projecteuclid.org/euclid.ijm/1256046803

Digital Object Identifier
doi:10.1215/ijm/1256046803

Mathematical Reviews number (MathSciNet)
MR650400

Zentralblatt MATH identifier
0466.31004

Subjects
Primary: 31A05: Harmonic, subharmonic, superharmonic functions
Secondary: 30E10: Approximation in the complex domain

#### Citation

Gamelin, T. W. Criteria for approximation by harmonic functions. Illinois J. Math. 26 (1982), no. 2, 353--357. doi:10.1215/ijm/1256046803. https://projecteuclid.org/euclid.ijm/1256046803