Constructive descriptions of functional classes by polynomial approximations. I, II (Q5941892)

Part I of the paper contains detailed proofs of two theorems announced earlier by the author in [Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 65, 199-202 (1976; Zbl 0356.30025); Dokl. Akad. Nauk SSSR 235, 546-549 (1977; Zbl 0379.30021)]. In part II the author describes a Hölder class of functions that are continuous on the closure and analytic in the interior of a Jordan domain in terms of the errors of polynomial approximation. The functions are approximated by properly chosen (``economically'' according to the notion of approximative entropy) families of polynomials.