Approximation of classes of analytic functions by algebraic polynomials and kolmogorov widths - Romanyuk, V. S. (Ukrains’kyi Matematychnyi Zhurnal, 1996)
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.