In this paper we prove a result on the Pompeiu problem. If the Schwarz
function PSI of the boundary of a simply-connected domain OMEGA subse
t-of R2 extends meromorphically into a certain portion E of OMEGA with
a pole at some point z0 is-an-element-of E, then OMEGA has the Pompei
u property unless PHI is a Mobius transformation, in which case OMEGA
is a disk.