Cover Image

Weighted approximation with varying weight /

Show other versions (1)

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...

Full description

Bibliographic Details
Main Author: Totik, V.
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin ; New York : Springer-Verlag, [1994]
Series:Lecture notes in mathematics (Springer-Verlag) ; 1569.
Subjects:
Approximation theory.
Polynomials.
analyse Fourier.
Théorie potentiel.
degré approximation.
inégalité.
approximation polynomiale.
approximation Padé.
polynôme.
approximation pondérée.
Approximation, Théorie de l'
Polynômes.
Benaderingen (wiskunde)
Polynomen.
Approximation, Théorie de l'.
Gewichtete Polynomapproximation.
Approximationstheorie.
Electronic books.
Online Access:Connect to the full text of this electronic book
Description
Summary: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.
Item Description:Electronic resource.
Physical Description:1 online resource (vi, 114 pages) : illustrations.
Format:Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Bibliography:Includes bibliographical references (pages [111]-114) and index.
ISBN:9783540483236 (electronic bk.)
3540483233 (electronic bk.)
ISSN:0075-8434 ;