General orthogonal polynomials:
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 th...
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1992
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| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 43 |
| Links: | https://doi.org/10.1017/CBO9780511759420 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (xii, 250 Seiten) |
| ISBN: | 9780511759420 |
Internformat
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| 100 | 1 | |a Stahl, Herbert | |
| 245 | 1 | 0 | |a General orthogonal polynomials |c Herbert Stahl, Vilmos Totik |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 1992 | |
| 300 | |a 1 Online-Ressource (xii, 250 Seiten) | ||
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| 490 | 1 | |a Encyclopedia of mathematics and its applications |v volume 43 | |
| 520 | |a 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. | ||
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| spelling | Stahl, Herbert General orthogonal polynomials Herbert Stahl, Vilmos Totik Cambridge Cambridge University Press 1992 1 Online-Ressource (xii, 250 Seiten) txt c cr Encyclopedia of mathematics and its applications volume 43 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. Totik, V. Erscheint auch als Druck-Ausgabe 9780521135047 Erscheint auch als Druck-Ausgabe 9780521415347 |
| spellingShingle | Stahl, Herbert General orthogonal polynomials |
| title | General orthogonal polynomials |
| title_auth | General orthogonal polynomials |
| title_exact_search | General orthogonal polynomials |
| title_full | General orthogonal polynomials Herbert Stahl, Vilmos Totik |
| title_fullStr | General orthogonal polynomials Herbert Stahl, Vilmos Totik |
| title_full_unstemmed | General orthogonal polynomials Herbert Stahl, Vilmos Totik |
| title_short | General orthogonal polynomials |
| title_sort | general orthogonal polynomials |
| work_keys_str_mv | AT stahlherbert generalorthogonalpolynomials AT totikv generalorthogonalpolynomials |