Weighted approximation with varying weights: The case of a power-type singularity

[摘要] 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.

[发布日期] 1996-12-01