Abstract

Let the integer and the modulus of continuity be fixed, and let be the class of all functions continuous on the closed unit disk , analytic on its interior , and having an -continuous th derivative on . Consider for each and each fixed the polynomial in (the st partial sum of the Taylor series of in a neighborhood of ). Then for any two points (1.1)Let be a closed subset of . This article contains a solution of the problem of free interpolation in , formulated as follows: find necessary and sufficient conditions on such that for each collection of th-degree polynomials satisfying conditions of the type (1.1) for all there is a function with .Bibliography: 13 titles.

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