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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.Read more
- The essential encyclopedic reference work on general orthogonal polynomials
- Intended for physicists as well as mathematicians
Reviews & endorsements
Review of the hardback: 'This is an important but difficult book.' Journal of Approximation TheorySee more reviews
Review of the hardback: 'This very clearly written book can be warmly recommended.' Acta Sci. Math.
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- Date Published: March 2010
- format: Paperback
- isbn: 9780521135047
- length: 268 pages
- dimensions: 229 x 152 x 15 mm
- weight: 0.4kg
- availability: Available
Table of Contents
1. Upper and lower bounds
2. Zero distribution of orthogonal polynomials
3. Regular n-th root asymptotic behaviour of orthogonal polynomials
4. Regularity criteria
Notes and bibliographical references
List of symbols
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