General Orthogonal Polynomials
1st Edition
Published on 11. May 2012
268 pages
978-1-139-24298-1 (ISBN)
Description
In this treatise, the authors present the general theory of orthogonal polynomials on the complex plane and several of its applications. The assumptions on the measure of orthogonality are general, the only restriction is that it has compact support on the complex plane. In the development of the theory the main emphasis is on asymptotic behaviour and the distribution of zeros. In the following chapters, the author explores the exact upper and lower bounds are given for the orthonormal polynomials and for the location of their zeros; regular n-th root asymptotic behaviour; and applications of the theory, including exact rates for convergence of rational interpolants, best rational approximants and non-diagonal Pade approximants to Markov functions (Cauchy transforms of measures). The results are based on potential theoretic methods, so both the methods and the results can be extended to extremal polynomials in norms other than L2 norms. A sketch of the theory of logarithmic potentials is given in an appendix.
Reviews / Votes
Review of the hardback: 'This is an important but difficult book.' Journal of Approximation Theory Review of the hardback: 'This very clearly written book can be warmly recommended.' Acta Sci. Math.More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
File size
9777,79 MB
ISBN-13
978-1-139-24298-1 (9781139242981)
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Schweitzer Classification
Other editions
Additional editions
Herbert Stahl | Vilmos Totik
General Orthogonal Polynomials
Book
03/2010
Cambridge University Press
€85.90
Shipment within 15-20 days
Herbert Stahl | Vilmos Totik
General Orthogonal Polynomials
Book
04/1992
Cambridge University Press
€154.00
Shipment within 15-20 days
Persons
Content
Introduction; 1. Upper and lower bounds; 2. Zero distribution of orthogonal polynomials; 3. Regular n-th root asymptotic behaviour of orthogonal polynomials; 4. Regularity criteria; 5. Localization; 6. Applications; Appendix; Notes and bibliographical references; Bibliography; List of symbols; Index.
