Convergence of Interpolating Laurent Polynomials on an Annulus

We study the convergence of Laurent polynomials that interpolate functions on the boundary of a circular annulus. The points of interpolation are chosen to be uniformly distributed on the two circles of the boundary. A maximal convergence theorem for functions analytic on the closure of the annulus is proved. We point out that, in general, there is no equiconvergence theorem between the interpolating Laurent polynomials and the partial sums of the Laurent expansion. The asymptotic behavior of the norm of the projection induced by the interpolating Laurent polynomials is established, which shows that the interpolating Laurent polynomials are near-minimax approximations.