General orthogonal polynomials
Author(s)
Bibliographic Information
General orthogonal polynomials
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 43）
Cambridge University Press, 1992
Available at / 99 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc20:515/st142070234823
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Note
Includes bibliographical references (p. [243]-248) and index
XISBN from "Transferred to digital printing 2009"
Description and Table of Contents
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.
Table of Contents
- 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.
by "Nielsen BookData"
