Best approximation of reproducing kernels of spaces of analytic functions

Abstract

We obtain exact values for the best approximation of a reproducing kernel of a system of p-Faber polynomials by functions of the Hardy space H _q, p ^-1 + q ^-1 = 1 and a Szegö reproducing kernel of the space E ²(Ω) in a simply connected domain Ω with rectifiable boundary.