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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1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Cambridge
Cambridge University Press
1992
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Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 43 |
Schlagworte: | |
Online-Zugang: | BSB01 FHN01 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: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
Beschreibung: | 1 online resource (xii, 250 pages) |
ISBN: | 9780511759420 |
DOI: | 10.1017/CBO9780511759420 |
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245 | 1 | 0 | |a General orthogonal polynomials |c Herbert Stahl, Vilmos Totik |
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490 | 0 | |a Encyclopedia of mathematics and its applications |v volume 43 | |
500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
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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Datensatz im Suchindex
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author | Stahl, Herbert |
author_facet | Stahl, Herbert |
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dewey-ones | 515 - Analysis |
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discipline | Mathematik |
doi_str_mv | 10.1017/CBO9780511759420 |
format | Electronic eBook |
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id | DE-604.BV043941690 |
illustrated | Not Illustrated |
indexdate | 2024-07-10T07:39:16Z |
institution | BVB |
isbn | 9780511759420 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350660 |
oclc_num | 849792277 |
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owner_facet | DE-12 DE-92 |
physical | 1 online resource (xii, 250 pages) |
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publishDate | 1992 |
publishDateSearch | 1992 |
publishDateSort | 1992 |
publisher | Cambridge University Press |
record_format | marc |
series2 | Encyclopedia of mathematics and its applications |
spelling | Stahl, Herbert Verfasser aut General orthogonal polynomials Herbert Stahl, Vilmos Totik Cambridge Cambridge University Press 1992 1 online resource (xii, 250 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 43 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 Orthogonal polynomials Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Orthogonale Polynome (DE-588)4172863-4 s 1\p DE-604 Totik, V. Sonstige oth Erscheint auch als Druckausgabe 978-0-521-13504-7 Erscheint auch als Druckausgabe 978-0-521-41534-7 https://doi.org/10.1017/CBO9780511759420 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Stahl, Herbert General orthogonal polynomials Orthogonal polynomials Orthogonale Polynome (DE-588)4172863-4 gnd |
subject_GND | (DE-588)4172863-4 |
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 Orthogonale Polynome (DE-588)4172863-4 gnd |
topic_facet | Orthogonal polynomials Orthogonale Polynome |
url | https://doi.org/10.1017/CBO9780511759420 |
work_keys_str_mv | AT stahlherbert generalorthogonalpolynomials AT totikv generalorthogonalpolynomials |