An optimal recovery view of Walsh's equiconvergence theorem

Abstract

J. L. Walsh showed that the differences of the partial sums of a function analytic only in a disk of radius ρ{variant} (>1) and the polynomials (of the same degrees) interpolating the function in roots of unity, converge to zero in |z| < ρ{variant}2. We reinterpret this problem in the context of analytic complexity, and examine it from that viewpoint. © 1987.