Journal of mathematical analysis and applications vol:204 issue:2 pages:409-418
The class of functions that can be uniformly approximated by weighted polynomials of the form w^n P_n with deg P_n less than or equal to n, depends on the behavior of the extremal measure associated with w as introduced by Mhaskar and Saff. It is shown that if in a neighborhood of a point to the extremal measure has a density with a power-type singularity at t_0, then every uniform limit vanishes at t_0. This complements results of Totik for continuous positive densities and Kuijlaars for densities that vanish at t_0. (C) 1996 Academic Press, Inc.