Supplement to the Mergelyan Theorem on the Denseness of Algebraic Polynomials in the Space $C_w^0$

Abstract

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.