General orthogonal polynomials / Herbert Stahl, Vilmos Totik

Auteur: Stahl, Herbert (1942-2013) - AuteurCo-auteur: Totik, Vilmos (1954-) - AuteurType de document: MonographieCollection: Encyclopedia of mathematics and its applications ; 43Langue: anglaisPays: Grande BretagneÉditeur: Cambridge : Cambridge university press, impr. 2010Description: 1 vol. (XII-250 p.) ; 23 cm ISBN: 9780521135047 ; br. Résumé: 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. (Source : CUP).Bibliographie: Bibliogr. p. 243-248. Index. Sujets MSC: 33C50 Special functions (33-XX deals with the properties of functions as functions) -- Hypergeometric functions -- Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
42C05 Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Orthogonal functions and polynomials, general theory
En-ligne: Zentralblatt | CUP
Location Call Number Status Date Due
Salle R 12153-01 / 33 STA (Browse Shelf) Available

Autre tirage : 1992

Bibliogr. p. 243-248. Index

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. (Source : CUP)

There are no comments for this item.

Log in to your account to post a comment.
Languages: English | Français | |