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Strong Asymptotics for Extremal Polynomials Associated with Weights on R

  • Book
  • © 1988

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Authors:
  1. Doron S. Lubinsky
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  2. Edward B. Saff
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1305)

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-VII
    Download chapter PDF

  2. Introduction

    • Doron S. Lubinsky, Edward B. Saff
    Pages 1-11

  3. Notation and index of notation

    • Doron S. Lubinsky, Edward B. Saff
    Pages 12-16

  4. Statement of main results

    • Doron S. Lubinsky, Edward B. Saff
    Pages 17-23

  5. Weighted polynomials and zeros of extremal polynomials

    • Doron S. Lubinsky, Edward B. Saff
    Pages 24-27

  6. Integral equations

    • Doron S. Lubinsky, Edward B. Saff
    Pages 28-39

  7. Polynomial approximation of potentials

    • Doron S. Lubinsky, Edward B. Saff
    Pages 40-48

  8. Infinite-finite range inequalities and their sharpness

    • Doron S. Lubinsky, Edward B. Saff
    Pages 49-56

  9. The largest zeros of extremal polynomials

    • Doron S. Lubinsky, Edward B. Saff
    Pages 57-66

  10. Further properties of Un, R(x)

    • Doron S. Lubinsky, Edward B. Saff
    Pages 67-72

  11. Nth root asymptotics for extremal polynomials

    • Doron S. Lubinsky, Edward B. Saff
    Pages 73-79

  12. Approximation by certain weighted polynomials, I

    • Doron S. Lubinsky, Edward B. Saff
    Pages 80-90

  13. Approximation by certain weighted polynomials, II

    • Doron S. Lubinsky, Edward B. Saff
    Pages 91-110

  14. Bernstein's formula and bernstein extremal polynomials

    • Doron S. Lubinsky, Edward B. Saff
    Pages 111-119

  15. Proof of the asymptotics for Enp(W)

    • Doron S. Lubinsky, Edward B. Saff
    Pages 120-127

  16. Proof of the asymptotics for the Lp extremal polynomials

    • Doron S. Lubinsky, Edward B. Saff
    Pages 128-135

  17. The case p=2 : Orthonormal polynomials

    • Doron S. Lubinsky, Edward B. Saff
    Pages 136-145

  18. Back Matter

    Pages 146-153
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Keywords

About this book

0. The results are consequences of a strengthened form of the following assertion: Given 0 1. Auxiliary results include inequalities for weighted polynomials, and zeros of extremal polynomials. The monograph is fairly self-contained, with proofs involving elementary complex analysis, and the theory of orthogonal and extremal polynomials. It should be of interest to research workers in approximation theory and orthogonal polynomials.

Bibliographic Information

  • Book Title: Strong Asymptotics for Extremal Polynomials Associated with Weights on R

  • Authors: Doron S. Lubinsky, Edward B. Saff

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0082413

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-18958-9Published: 09 March 1988

  • eBook ISBN: 978-3-540-38857-9Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 156

  • Topics: Numerical Analysis

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