  Walsh introduced a generalisation of Faber polynomials to certain compact
sets which need not be connected. We derive several equivalent representations
of these Faber-Walsh polynomials, analogous to representations of Faber
polynomials. Some simple asymptotic properties of the Faber-Walsh polynomials
on the complement of the compact set are established. We further show that
suitably normalised Faber-Walsh polynomials are asymptotically optimal
polynomials in the sense of [Eiermann and Niethammer 1983].
