Orthogonal rational functions:
This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lo...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1999
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| Schriftenreihe: | Cambridge monographs on applied and computational mathematics
5 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xiv, 407 pages) |
| ISBN: | 9780511530050 |
| DOI: | 10.1017/CBO9780511530050 |
Internformat
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| 100 | 1 | |a Bultheel, Adhemar |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Orthogonal rational functions |c Adhemar Bultheel [and others] |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 1999 | |
| 300 | |a 1 online resource (xiv, 407 pages) | ||
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| 490 | 0 | |a Cambridge monographs on applied and computational mathematics |v 5 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a 1. Preliminaries -- 2. The fundamental spaces -- 3. The kernel functions -- 4. Recurrence and second kind functions -- 5. Para-orthogonality and quadrature -- 6. Interpolation -- 7. Density of the rational functions -- 8. Favard theorems -- 9. Convergence -- 10. Moment problems -- 11. The boundary case -- 12. Some applications | |
| 520 | |a This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering | ||
| 650 | 4 | |a Functions, Orthogonal | |
| 650 | 4 | |a Functions of complex variables | |
| 650 | 0 | 7 | |a Mehrere komplexe Variable |0 (DE-588)4169285-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 0 | |a Orthogonale Funktionen |0 (DE-588)4475233-7 |D s |
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Datensatz im Suchindex
| _version_ | 1804176882745212928 |
|---|---|
| any_adam_object | |
| author | Bultheel, Adhemar |
| author_facet | Bultheel, Adhemar |
| author_role | aut |
| author_sort | Bultheel, Adhemar |
| author_variant | a b ab |
| building | Verbundindex |
| bvnumber | BV043941269 |
| classification_rvk | SK 680 SK 780 |
| collection | ZDB-20-CBO |
| contents | 1. Preliminaries -- 2. The fundamental spaces -- 3. The kernel functions -- 4. Recurrence and second kind functions -- 5. Para-orthogonality and quadrature -- 6. Interpolation -- 7. Density of the rational functions -- 8. Favard theorems -- 9. Convergence -- 10. Moment problems -- 11. The boundary case -- 12. Some applications |
| ctrlnum | (ZDB-20-CBO)CR9780511530050 (OCoLC)849959315 (DE-599)BVBBV043941269 |
| dewey-full | 515/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.55 |
| dewey-search | 515/.55 |
| dewey-sort | 3515 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511530050 |
| format | Electronic eBook |
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| id | DE-604.BV043941269 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:15Z |
| institution | BVB |
| isbn | 9780511530050 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350240 |
| oclc_num | 849959315 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xiv, 407 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge monographs on applied and computational mathematics |
| spelling | Bultheel, Adhemar Verfasser aut Orthogonal rational functions Adhemar Bultheel [and others] Cambridge Cambridge University Press 1999 1 online resource (xiv, 407 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge monographs on applied and computational mathematics 5 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 1. Preliminaries -- 2. The fundamental spaces -- 3. The kernel functions -- 4. Recurrence and second kind functions -- 5. Para-orthogonality and quadrature -- 6. Interpolation -- 7. Density of the rational functions -- 8. Favard theorems -- 9. Convergence -- 10. Moment problems -- 11. The boundary case -- 12. Some applications This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering Functions, Orthogonal Functions of complex variables Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Orthogonale Funktionen (DE-588)4475233-7 gnd rswk-swf Orthogonale Funktionen (DE-588)4475233-7 s Mehrere komplexe Variable (DE-588)4169285-8 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-11591-9 Erscheint auch als Druckausgabe 978-0-521-65006-9 https://doi.org/10.1017/CBO9780511530050 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bultheel, Adhemar Orthogonal rational functions 1. Preliminaries -- 2. The fundamental spaces -- 3. The kernel functions -- 4. Recurrence and second kind functions -- 5. Para-orthogonality and quadrature -- 6. Interpolation -- 7. Density of the rational functions -- 8. Favard theorems -- 9. Convergence -- 10. Moment problems -- 11. The boundary case -- 12. Some applications Functions, Orthogonal Functions of complex variables Mehrere komplexe Variable (DE-588)4169285-8 gnd Orthogonale Funktionen (DE-588)4475233-7 gnd |
| subject_GND | (DE-588)4169285-8 (DE-588)4475233-7 |
| title | Orthogonal rational functions |
| title_auth | Orthogonal rational functions |
| title_exact_search | Orthogonal rational functions |
| title_full | Orthogonal rational functions Adhemar Bultheel [and others] |
| title_fullStr | Orthogonal rational functions Adhemar Bultheel [and others] |
| title_full_unstemmed | Orthogonal rational functions Adhemar Bultheel [and others] |
| title_short | Orthogonal rational functions |
| title_sort | orthogonal rational functions |
| topic | Functions, Orthogonal Functions of complex variables Mehrere komplexe Variable (DE-588)4169285-8 gnd Orthogonale Funktionen (DE-588)4475233-7 gnd |
| topic_facet | Functions, Orthogonal Functions of complex variables Mehrere komplexe Variable Orthogonale Funktionen |
| url | https://doi.org/10.1017/CBO9780511530050 |
| work_keys_str_mv | AT bultheeladhemar orthogonalrationalfunctions |