Lecture Notes in Mathematics

Asymptotics for Orthogonal Polynomials

Authors: Van Assche, Walter

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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.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-540-47711-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA in USD
  • ISBN 978-3-540-18023-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Asymptotics for Orthogonal Polynomials
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1265
Copyright
1987
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-47711-2
DOI
10.1007/BFb0081880
Softcover ISBN
978-3-540-18023-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VI, 206
Topics