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Weighted Approximation with Varying Weight

  • Authors
  • VilmosĀ Totik

Part of the Lecture Notes in Mathematics book series (LNM, volume 1569)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Vilmos Totik
    Pages 1-5
  3. Vilmos Totik
    Pages 7-20
  4. Vilmos Totik
    Pages 21-48
  5. Vilmos Totik
    Pages 49-77
  6. Vilmos Totik
    Pages 79-110
  7. Back Matter
    Pages 111-115

About this book

Introduction

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.

Keywords

Approximation Logarithmic potentials Pade approximation Varying Weight orthogonal Polynomials

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0076133
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-57705-8
  • Online ISBN 978-3-540-48323-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site