Asymptotics for Orthogonal Polynomials

Walter van Assche

ISBN 10: 3540180230 / ISBN 13: 9783540180234

Published by Springer Vieweg, Springer, 1987

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783540180234

Bibliographic Details

• Title: Asymptotics for Orthogonal Polynomials
• Publisher: Springer Vieweg, Springer
• Publication Date: 1987
• Language: English
• ISBN 10: 3540180230
• ISBN 13: 9783540180234
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 254W x 178H x 12D millimeters 254 millimeters width by 178 millimeters height by 12 millimeters depth
• Weight: 416 grams

About this title

Synopsis

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.