General Orthogonal Polynomials

Herbert Stahl; Vilmos Totik

doi:10.1017/CBO9780511759420

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General Orthogonal Polynomials

General Orthogonal Polynomials

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This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

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Herbert Stahl, Technische Fachhochschule, Berlin, Vilmos Totik, University of South Florida

Publisher: Cambridge University Press
Online publication date: August 2010
Print publication year: 1992
Online ISBN: 9780511759420
DOI: https://doi.org/10.1017/CBO9780511759420

Subjects: Mathematics (general), Mathematics, Algebra
Series: Encyclopedia of Mathematics and its Applications (43)

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General Orthogonal Polynomials
Herbert Stahl, Vilmos Totik
Online ISBN: 9780511759420

Book DOI: https://doi.org/10.1017/CBO9780511759420
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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.

Review of the hardback:‘This is an important but difficult book.’

Source: Journal of Approximation Theory

Review of the hardback:‘This very clearly written book can be warmly recommended.’

Source: Acta Sci. Math.

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General Orthogonal Polynomials

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-ix

Acknowledgments
pp x-x

Symbols
pp xi-xii

1 - Upper and Lower Bounds
pp 1-29

2 - Zero Distribution of Orthogonal Polynomials
pp 30-58

3 - Regular nth-root Asymptotic Behavior of Orthonormal Polynomials
pp 59-99

4 - Regularity Criteria
pp 100-137

5 - Localization
pp 138-148

6 - Applications
pp 149-219

Appendix
pp 220-234

Notes and Bibliographical References
pp 235-242

Bibliography
pp 243-248

Index
pp 249-250

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