Weighted Approximation with Varying Weight (Paperback, 1994 ed.)

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.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Lecture Notes in Mathematics, 1569
Release date:	February 1994
First published:	1994
Authors:	Vilmos Totik
Dimensions:	235 x 155 x 6mm (L x W x T)
Format:	Paperback
Pages:	118
Edition:	1994 ed.
ISBN-13:	978-3-540-57705-8
Categories:	Books > Science & Mathematics > Mathematics > Applied mathematics > General
LSN:	3-540-57705-X
Barcode:	9783540577058

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