General Orthogonal Polynomials (Encyclopedia of Math and its Applications)


General Orthogonal Polynomials (Encyclopedia of Math and its Applications)

  • 提携先の海外書籍取次会社に在庫がございます。通常2週間で発送いたします。
    1. 納期遅延や、ご入手不能となる場合が若干ございます。
    2. 複数冊ご注文の場合、分割発送となる場合がございます。
    3. 美品のご指定は承りかねます。
  • ≪洋書のご注文につきまして≫ 「海外取次在庫あり」および「国内仕入れ先からお取り寄せいたします」表示の商品でも、納期の目安期間内にお届けできないことがございます。あらかじめご了承ください。

  • 製本 Hardcover:ハードカバー版/ページ数 250 p.
  • 言語 ENG
  • 商品コード 9780521415347
  • DDC分類 515.55


New in paperback. Hardcover was published in 1992.

Full 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

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
Notes and bibliographical references
List of symbols