Weighted Approximation with Varying Weights: The Case of a Power-Type Singularity

✍ Scribed by A.B.J. Kuijlaars

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 145 KB
• Volume: 204
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1996.0444

✦ Synopsis

The class of functions that can be uniformly approximated by weighted polynomials of the form w n P with deg P F n, depends on the behavior of the extremal n n measure associated with w as introduced by Mhaskar and Saff. It is shown that if in a neighborhood of a point t the extremal measure has a density with a power-type 0 singularity at t , then every uniform limit vanishes at t . This complements results 0 0

of Totik for continuous positive densities and Kuijlaars for densities that vanish at t .