Weighted approximation with varying weight : WnPn. Lecture notes in mathematics ; Vol. 1569

Totik, Vilmos,

ISBN 10: 354057705X / ISBN 13: 9783540577058

Published by Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest : Springer, 1994

About this Item

VI, 114 pages Ex-Library book in very good condition. 9783540577058 Sprache: Englisch Gewicht in Gramm: 249.

Seller Inventory # 1166239

Bibliographic Details

• Title: Weighted approximation with varying weight : WnPn. Lecture notes in mathematics ; Vol. 1569
• Publisher: Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest : Springer
• Publication Date: 1994
• Language: English
• ISBN 10: 354057705X
• ISBN 13: 9783540577058
• Binding: Soft cover
• Seller catalogs:
  • SA MATHEMATIK

About this title

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.