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: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [England] ; New York :
Cambridge University Press,
1992.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 43. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| 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. |
| Beschreibung: | 1 online resource (xii, 250 pages) |
| Bibliographie: | Includes bibliographical references (pages 243-248) and index. |
| ISBN: | 9781107088306 1107088305 |
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| 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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| illustrated | Not Illustrated |
| indexdate | 2024-10-25T16:21:39Z |
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| isbn | 9781107088306 1107088305 |
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| spelling | Stahl, Herbert. General orthogonal polynomials / Herbert Stahl, Vilmos Totik. Cambridge [England] ; New York : Cambridge University Press, 1992. 1 online resource (xii, 250 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; volume 43 Includes bibliographical references (pages 243-248) and index. Print version record. 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. A. VII BalayageA. VIII Green Potential and Condenser Capacity; A. IX The Energy Problem in the Presence of an External Field; Notes and Bibliographical References; Bibliography; Index Orthogonal polynomials. http://id.loc.gov/authorities/subjects/sh85095794 Polynômes orthogonaux. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Orthogonal polynomials fast Polynômes orthogonaux. ram Totik, V. has work: General orthogonal polynomials (Text) https://id.oclc.org/worldcat/entity/E39PCGGjyMMdjx7YrtCYGhfwYd https://id.oclc.org/worldcat/ontology/hasWork Print version: Stahl, Herbert. General orthogonal polynomials 0521415349 (DLC) 91027733 (OCoLC)24219180 Encyclopedia of mathematics and its applications ; v. 43. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569331 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569331 Volltext |
| spellingShingle | Stahl, Herbert General orthogonal polynomials / Encyclopedia of mathematics and its applications ; A. VII BalayageA. VIII Green Potential and Condenser Capacity; A. IX The Energy Problem in the Presence of an External Field; Notes and Bibliographical References; Bibliography; Index Orthogonal polynomials. http://id.loc.gov/authorities/subjects/sh85095794 Polynômes orthogonaux. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Orthogonal polynomials fast Polynômes orthogonaux. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85095794 |
| 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 |
| topic | Orthogonal polynomials. http://id.loc.gov/authorities/subjects/sh85095794 Polynômes orthogonaux. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Orthogonal polynomials fast Polynômes orthogonaux. ram |
| topic_facet | Orthogonal polynomials. Polynômes orthogonaux. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Orthogonal polynomials |
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