Weighted Approximation with Varying Weight (Paperback)

Vilmos Totik

ISBN 10: 354057705X / ISBN 13: 9783540577058

Published by Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 1994

Paperback. This monograph offers a new construction for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form wn Pn. The new technique settles several open problems. It leads to a simple proof for the strong asymptotics on some Lp 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 to yield (in a sense) uniformly good approximation on the whole support. This allows the reader to deduce strong asymptotics in some Lp extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behaviour of orthogonal polynomials and multipoint Pade approximation. The new techniquesettles several open problems, and it leads to a simpleproof 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- typeasymptotics for the leading coefficients of thecorresponding orthogonal polynomials. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9783540577058

Synopsis:

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.

Bibliographic Details

Title: Weighted Approximation with Varying Weight (...
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin
Publication Date: 1994
Binding: Paperback
Condition: new