Polynomial approximation avoiding values in countable sets

Johan Andersson; Linnea Rousu

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arXiv · 1907.00204

Polynomial approximation avoiding values in countable sets

Johan Andersson·Linnea Rousu

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Abstract

We generalize a version of Lavrent\'ev's theorem which says that a function that is continuous on a compact set K with connected complement and without interior points can be uniformly approximated as closely as desired by a polynomial without zeros on the set K, so that the polynomial can avoid values from any given countable set. We also prove a corresponding version of Mergelyan's theorem when the interior of K is a finite union of Jordan domains, pairwise separated by a positive distance.

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Johan Andersson, Linnea Rousu. 2019-06-29. Polynomial approximation avoiding values in countable sets. https://arxiv.org/abs/1907.00204

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