Approximation of classes of analytic functions by algebraic polynomials and kolmogorov widths

Abstract

We obtain estimates of the best polynomial approximations, uniform in the closure $B$ of Faber domains of the complex plane $ℂ$, for functions continuous in $B$ and defined by Cauchy-type integrals with densities possessing certain generalized differential properties. We establish estimates exact in order for the Kolmogorov widths of classes of such functions in relevant functional spaces.