Hidden Bibliographic Details
| Other authors / contributors: | Assche, Walter van, 1958-
|
|---|
| ISBN: | 9783540477112
354047711X
0387180230
9780387180236
|
|---|
| Notes: | Includes bibliographical references (pages 181-195) and index.
Restrictions unspecified
Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212
digitized 2010 HathiTrust Digital Library committed to preserve
Print version record.
|
|---|
| Summary: | 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 Schrdinger operators, illustrating the close interaction with different branches of applied mathematics.
|
|---|
| Other form: | Print version: Assche, Walter van, 1958- Asymptotics for orthogonal polynomials. Berlin ; New York : Springer-Verlag, ©1987 0387180230
|
|---|
