Vladimir Andrievskii

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We construct polynomial approximations of Dzjadyk type (in terms of the k -th modulus of continuity, k ≥ 1 ) for analytic functions defined on a continuum E in the complex plane, which simultaneously interpolate at given points of E . Furthermore, the error in this approximation is decaying as e−cn α strictly inside E , where c and α are positive constants(More)
We study the uniform approximation of the canonical conformal mapping, for a Jordan domain onto the unit disk, by polynomials generated from the partial sums of the Szegő kernel expansion. These polynomials converge to the conformal mapping uniformly on the closure of any Smirnov domain. We prove estimates for the rate of such convergence on domains with(More)