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Weighted Approximation with Varying Weight

  • Book
  • © 1994

Overview

Authors:
  1. Vilmos Totik
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1569)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-VI
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  2. Introduction

    • Vilmos Totik
    Pages 1-5

  3. Freud weights

    • Vilmos Totik
    Pages 7-20

  4. Approximation with general weights

    • Vilmos Totik
    Pages 21-48

  5. Varying weights

    • Vilmos Totik
    Pages 49-77

  6. Applications

    • Vilmos Totik
    Pages 79-110

  7. Back Matter

    Pages 111-115
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Keywords

About this book

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 Information

  • Book Title: Weighted Approximation with Varying Weight

  • Authors: Vilmos Totik

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0076133

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Softcover ISBN: 978-3-540-57705-8Published: 28 February 1994

  • eBook ISBN: 978-3-540-48323-6Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 118

  • Topics: Real Functions, Potential Theory

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