Simultaneous approximation and interpolation of functions on continua in the complex plane

V. V. Andrievskii; I. E. Pritsker; R. S. Varga

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Simultaneous approximation and interpolation of functions on continua in the complex plane

V. V. Andrievskii·I. E. Pritsker·R. S. Varga

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Abstract

We construct polynomial approximations of Dzjadyk type (in terms of the k-th modulus of continuity, $k \ge 1$) 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 $e^{-cn^\alpha}$ strictly inside E, where c and $\alpha$ are positive constants independent of the degree n of the approximating polynomial.

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V. V. Andrievskii, I. E. Pritsker, R. S. Varga. 2000-05-03. Simultaneous approximation and interpolation of functions on continua in the complex plane. https://arxiv.org/abs/math/0005032

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