UNIVERSITY OF CRETE - DEPARTMENT OF MATHEMATICS
Knossos Ave., GR 714 09 Iraklio, Crete, Greece, Tel: +30 2810393800, Fax: +30 2810393881

At first, several facts on closed function algebras on the unit circle will be recalled. In particular, Sarason's theorem will be discussed. The investigation of Sarason's type theorem in potential theory naturally leads to the following question: to what extent bounded harmonic functions on a domain can be uniformly approximated on by functions from , the space of continuous functions on the closure of and harmonic on . In order to answer this question, as an intermediate step, approximation of Perron-Wiener-Brelot solutions of the Dirichlet problem by functions from is studied. The talk is based on the joint work with W. Hansen (J.Approx.Theory,2003).