2001 | OriginalPaper | Chapter
Weighted Polynomial Approximation
Authors : Eli Levin, Doron S. Lubinsky
Published in: Orthogonal Polynomials for Exponential Weights
Publisher: Springer New York
Included in: Professional Book Archive
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
In this chapter, we establish the existence of weighted polynomial approximations that are a prerequisite to the estimates and asymptotics in subsequent chapters. We search for polynomials P n of degree n such that P n W approximates 1 in some sense on [a−n, a n ]. There are several approaches to this problem ([48], [86], [115], [136], [66], [178]), most based on discretisation of the potential. The most successful one has been given by Totik [178], and this is the method that we employ. Because of our need to approximate almost up to a ±n , our results do not follow from those in [178], [180], [182].