General Orthogonal Polynomials
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General Orthogonal Polynomials by Herbert Stahl
Book DescriptionIn 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.
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Book DetailsISBN: 9780521415347
(234mm x 156mm x 19mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 24-Apr-1992
Country of Publication: United Kingdom
Books By Author Herbert Stahl
General Orthogonal Polynomials, Paperback (March 2010)» View all books by Herbert Stahl
An encyclopedic presentation of general orthogonal polynomials, placing emphasis on asymptotic behaviour and zero distribution.
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