ENGLISH

Weighted Approximation with Varying Weight

By Vilmos Totik (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1994
ISBN
9780387577050, 0-387-57705-X, 354057705X
DOI
10.1007/BFb0076133
LCC
QA3 .L28 no. 1569,QA221 .L28 no. 1569
Open Library ID
OL1436919M
Language
english
Format
DJVU
Filesize
684 kB (700399 bytes)
Series
Lecture Notes in Mathematics 1569
Edition
1
Pages
118\118
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11
Real Functions; Potential Theory

Description

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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