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  3. General Orthogonal Polynomials
  • Cited by 209
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2010
      April 1992
      ISBN:
      9780511759420
      9780521415347
      9780521135047
      DOI:
      https://doi.org/10.1017/CBO9780511759420
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.512kg, 268 Pages
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.4kg, 268 Pages
      • Subjects:
      Mathematics (general), Mathematics, Algebra
      Series:
      Encyclopedia of Mathematics and its Applications (43)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    Encyclopedia of Mathematics and its Applications (43)
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    Book 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.

    Reviews

    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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