Weighted Approximation with Varying Weight

Weighted Approximation with Varying Weight
Author :
Publisher : Springer
Total Pages : 119
Release :
ISBN-10 : 9783540483236
ISBN-13 : 3540483233
Rating : 4/5 (233 Downloads)

Book Synopsis Weighted Approximation with Varying Weight by : Vilmos Totik

Download or read book Weighted Approximation with Varying Weight written by Vilmos Totik and published by Springer. This book was released on 2006-11-15 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.


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