Orthogonal rational functions:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
1999
|
| Ausgabe: | 1. publication |
| Schriftenreihe: | Cambridge Monographs on Applied and Computational Mathematics
5 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 407 Seiten graph. Darst. |
| ISBN: | 0521650062 |
Internformat
MARC
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| 245 | 1 | 0 | |a Orthogonal rational functions |c Adhemar Bultheel [und 3 andere] |
| 250 | |a 1. publication | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge University Press |c 1999 | |
| 300 | |a XIV, 407 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge Monographs on Applied and Computational Mathematics |v 5 | |
| 650 | 7 | |a Functies (wiskunde) |2 gtt | |
| 650 | 7 | |a Orthogonale reeksen |2 gtt | |
| 650 | 4 | |a Functions of complex variables | |
| 650 | 4 | |a Functions, Orthogonal | |
| 650 | 0 | 7 | |a Orthogonale Funktionen |0 (DE-588)4475233-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mehrere komplexe Variable |0 (DE-588)4169285-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Orthogonale Funktionen |0 (DE-588)4475233-7 |D s |
| 689 | 0 | 1 | |a Mehrere komplexe Variable |0 (DE-588)4169285-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Bultheel, Adhemar |e Sonstige |4 oth | |
| 830 | 0 | |a Cambridge Monographs on Applied and Computational Mathematics |v 5 |w (DE-604)BV011073737 |9 5 | |
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Datensatz im Suchindex
| _version_ | 1804127378390122496 |
|---|---|
| adam_text | Contents
List of symbols page xi
Introduction 1
1 Preliminaries 15
1.1 Hardy classes 15
1.2 The classes C and B 23
1.3 Factorizations 31
1.4 Reproducing kernel spaces 34
1.5 J unitary and J contractive matrices 36
2 The fundamental spaces 42
2.1 The spaces £„ 42
2.2 Calculus in £„ 53
2.3 Extremal problems in £„ 58
3 The kernel functions 64
3.1 Christoffel Darboux relations 64
3.2 Recurrence relations for the kernels 67
3.3 Normalized recursions for the kernels 70
4 Recurrence and second kind functions 74
4.1 Recurrence for the orthogonal functions 74
4.2 Functions of the second kind 82
4.3 General solutions 90
4.4 Continued fractions and three term recurrence 95
4.5 Points not on the boundary 101
vii
viii Contents
5 Para orthogonality and quadrature 106
5.1 Interpolatory quadrature 106
5.2 Para orthogonal functions 108
5.3 Quadrature 112
5.4 The weights 117
5.5 An alternative approach 119
6 Interpolation 121
6.1 Interpolation properties for orthogonal functions 121
6.2 Measures and interpolation 129
6.3 Interpolation properties for the kernels 135
6.4 The interpolation algorithm of Nevanlinna Pick 140
6.5 Interpolation algorithm for the orthonormal functions 145
7 Density of the rational functions 149
7.1 Density in Lp and Hp 149
7.2 Density in L2(ii) and H2(fJ.) 155
8 Favard theorems 161
8.1 Orthogonal functions 161
8.2 Kernels 165
9 Convergence 173
9.1 Generalization of the Szego problem 174
9.2 Further convergence results and asymptotic behavior 181
9.3 Convergence of p* 183
9.4 Equivalence of conditions 191
9.5 Varying measures 192
9.6 Stronger results 196
9.7 Weak convergence 206
9.8 Erdos Turan class and ratio asymptotics 208
9.9 Root asymptotics 226
9.10 Rates of convergence 233
10 Moment problems 239
10.1 Motivation and formulation of the problem 239
10.2 Nested disks 241
10.3 The moment problem 251
Contents ix
11 The boundary case 257
11.1 Recurrence for points on the boundary 257
11.2 Functions of the second kind 267
11.3 Christoffel Darboux relation 272
11.4 Green s formula 277
11.5 Quasi orthogonal functions 280
11.6 Quadrature formulas 286
11.7 Nested disks 290
11.8 Moment problem 300
11.9 Favard type theorem 307
11.10 Interpolation 319
11.11 Convergence 338
12 Some applications 342
12.1 Linear prediction 343
12.2 Pisarenko modeling problem 356
12.3 Lossless inverse scattering 359
12.4 Network synthesis 369
12.5 Hoc problems 373
12.5.1 The standard H^ control problem 373
12.5.2 Hankel operators 379
12.5.3 Hankel norm approximation 385
Conclusion 389
Bibliography 393
Index 405
|
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| id | DE-604.BV012714673 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:32:24Z |
| institution | BVB |
| isbn | 0521650062 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008643443 |
| oclc_num | 39534097 |
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| owner_facet | DE-20 DE-703 DE-634 DE-11 DE-188 |
| physical | XIV, 407 Seiten graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge Monographs on Applied and Computational Mathematics |
| series2 | Cambridge Monographs on Applied and Computational Mathematics |
| spelling | Orthogonal rational functions Adhemar Bultheel [und 3 andere] 1. publication Cambridge [u.a.] Cambridge University Press 1999 XIV, 407 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge Monographs on Applied and Computational Mathematics 5 Functies (wiskunde) gtt Orthogonale reeksen gtt Functions of complex variables Functions, Orthogonal Orthogonale Funktionen (DE-588)4475233-7 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Orthogonale Funktionen (DE-588)4475233-7 s Mehrere komplexe Variable (DE-588)4169285-8 s DE-604 Bultheel, Adhemar Sonstige oth Cambridge Monographs on Applied and Computational Mathematics 5 (DE-604)BV011073737 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008643443&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Orthogonal rational functions Cambridge Monographs on Applied and Computational Mathematics Functies (wiskunde) gtt Orthogonale reeksen gtt Functions of complex variables Functions, Orthogonal Orthogonale Funktionen (DE-588)4475233-7 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| subject_GND | (DE-588)4475233-7 (DE-588)4169285-8 |
| title | Orthogonal rational functions |
| title_auth | Orthogonal rational functions |
| title_exact_search | Orthogonal rational functions |
| title_full | Orthogonal rational functions Adhemar Bultheel [und 3 andere] |
| title_fullStr | Orthogonal rational functions Adhemar Bultheel [und 3 andere] |
| title_full_unstemmed | Orthogonal rational functions Adhemar Bultheel [und 3 andere] |
| title_short | Orthogonal rational functions |
| title_sort | orthogonal rational functions |
| topic | Functies (wiskunde) gtt Orthogonale reeksen gtt Functions of complex variables Functions, Orthogonal Orthogonale Funktionen (DE-588)4475233-7 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| topic_facet | Functies (wiskunde) Orthogonale reeksen Functions of complex variables Functions, Orthogonal Orthogonale Funktionen Mehrere komplexe Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008643443&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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