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Asymptotics for Orthogonal Polynomials

  • Book
  • © 1987

Overview

Authors:
  1. Walter Assche
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1265)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-VI
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  2. Introduction

    • Walter Van Assche
    Pages 1-13

  3. Orthogonal polynomials on a compact set

    • Walter Van Assche
    Pages 14-42

  4. Asymptotically periodic recurrence coefficients

    • Walter Van Assche
    Pages 43-86

  5. Probabilistic proofs of asymptotic formulas

    • Walter Van Assche
    Pages 87-104

  6. Orthogonal polynomials on unbounded sets

    • Walter Van Assche
    Pages 105-137

  7. Zero distribution and consequences

    • Walter Van Assche
    Pages 138-163

  8. Some applications

    • Walter Van Assche
    Pages 164-174

  9. Back Matter

    Pages 175-201
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Keywords

About this book

Recently there has been a great deal of interest in the theory of orthogonal polynomials. The number of books treating the subject, however, is limited. This monograph brings together some results involving the asymptotic behaviour of orthogonal polynomials when the degree tends to infinity, assuming only a basic knowledge of real and complex analysis. An extensive treatment, starting with special knowledge of the orthogonality measure, is given for orthogonal polynomials on a compact set and on an unbounded set. Another possible approach is to start from properties of the coefficients in the three-term recurrence relation for orthogonal polynomials. This is done using the methods of (discrete) scattering theory. A new method, based on limit theorems in probability theory, to obtain asymptotic formulas for some polynomials is also given. Various consequences of all the results are described and applications are given ranging from random matrices and birth-death processes to discrete Schrödinger operators, illustrating the close interaction with different branches of applied mathematics.

Bibliographic Information

  • Book Title: Asymptotics for Orthogonal Polynomials

  • Authors: Walter Assche

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0081880

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • Softcover ISBN: 978-3-540-18023-4Published: 24 June 1987

  • eBook ISBN: 978-3-540-47711-2Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 206

  • Topics: Analysis

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