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Asymptotics for Orthogonal Polynomials

  • Authors
  • Walter Van Assche

Part of the Lecture Notes in Mathematics book series (LNM, volume 1265)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Walter Van Assche
    Pages 1-13
  3. Walter Van Assche
    Pages 14-42
  4. Walter Van Assche
    Pages 43-86
  5. Walter Van Assche
    Pages 87-104
  6. Walter Van Assche
    Pages 105-137
  7. Walter Van Assche
    Pages 138-163
  8. Walter Van Assche
    Pages 164-174
  9. Back Matter
    Pages 175-201

About this book

Introduction

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.

Keywords

applied mathematics complex analysis distribution measure orthogonal polynomials scattering theory schrödinger operator

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0081880
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-18023-4
  • Online ISBN 978-3-540-47711-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site