Mergelyan's theorem for zero free functions

JOURNAL OF APPROXIMATION THEORY

卷:169

Article

Khrushchev, Sergey

关键词: Mergelyan's theorem;    Polynomial approximation;    Logarithmically continuous functions;    Locally connected compact sets;    Peano spaces;   

DOI  :  10.1016/j.jat.2013.01.003

来源: Elsevier

【 摘 要 】

The paper gives a partial answer to a question posed by Johan Andersson and Paul Gauthier. Namely, we prove that every function f continuous on a locally connected compact set K with connected complement, analytic in its interior and not vanishing in the interior can be approximated by polynomials with zeros outside of K. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free