Supplement to the Mergelyan Theorem on the Denseness of Algebraic Polynomials in the Space $C_w^0$
We give a supplement to the theorem on the denseness of polynomials in the space $C_w^0$ established by Mergelyan in 1956 for the case where algebraic polynomials are dense in $C_w^0$. In the case indicated, we give a complete description of all functions that can be approximated by algebraic polynomials in seminorm.
English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 7, pp 1021-1034.
Citation Example: Bakan A. G. Supplement to the Mergelyan Theorem on the Denseness of Algebraic Polynomials in the Space $C_w^0$ // Ukr. Mat. Zh. - 2005. - 57, № 7. - pp. 867–878.