J-contractive matrix valued functions and related topics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
116 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 575 S. |
| ISBN: | 0521883008 9780521883009 |
Internformat
MARC
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| 100 | 1 | |a Arov, Damir Z. |d 1934- |e Verfasser |0 (DE-588)172974356 |4 aut | |
| 245 | 1 | 0 | |a J-contractive matrix valued functions and related topics |c Damir Z. Arov and Harry Dym |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a XI, 575 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Encyclopedia of mathematics and its applications |v 116 | |
| 650 | 0 | 7 | |a Matrixwertige Funktion |0 (DE-588)4128928-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Matrixwertige Funktion |0 (DE-588)4128928-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Dym, Harry |d 1938- |e Sonstige |0 (DE-588)124041205 |4 oth | |
| 830 | 0 | |a Encyclopedia of mathematics and its applications |v 116 |w (DE-604)BV000903719 |9 116 | |
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Datensatz im Suchindex
| _version_ | 1804142693656297472 |
|---|---|
| adam_text | Contents
Preface page xi
1 Introduction 1
2 Algebraic preliminaries 13
2.1 The classes Vconst(J) and Uconst(J) 13
2.2 The Potapov-Ginzburg transform 14
2.3 Linear fractional transformations 24
2.4 Matrix balls 30
2.5 Redheffer transforms 34
2.6 Indefinite metrics in the space Cm 37
2.7 Minus matrices 45
2.8 Strictly minus matrices 48
2.9 Linear fractional transformations in Sp^st 58
2.10 Linear fractional transformations in C^pst 63
2.11 Transformations from Sp*npst into Cpc*pst 66
2.12 Affine generalizations 68
2.13 The J modulus 72
2.14 Infinite products of matrices 77
2.15 Some useful inequalities 80
2.16 Bibliographical notes 81
3 The Nevanlinna class of meromorphic mvf s 83
3.1 Basic classes of functions 83
3.2 The Riesz-Herglotz-Nevanlinna representation 87
3.3 Some subclasses of the Carathéodory class Cpxp 91
3.4 Inner-outer factorization in the class Hoo 93
3.5 Factorization in the classes M+ and Af 98
3.6 The rank of meromorphic mvf s 103
3.7 Inner and outer mvf s in Hg* 104
vii
via Contents
3.8 Fourier transforms and Paley-Wiener theorems 105
3.9 The Beurling-Lax theorem 107
3.10 Inner-outer factorization in Hp£q 114
3.11 The Smirnov maximum principle 118
3.12 Characterization via multiplication operators 122
3.13 Factorization in fifpxg and denominators 126
3.14 Some properties of outer mvf s 133
3.15 Scalar denominators 136
3.16 Factorization of positive semidefinite mvf s 138
3.17 Blaschke-Potapov products in SpXp 142
3.18 Entire matrix functions of class Mpxq 147
3.19 Entire inner mvf s 151
3.20 Minimal denominators of mvf s / G £ D Npxq 155
3.21 The class Wxq 157
3.22 Mean types for mvf s in Afpxq and Wxq 163
3.23 Bibliographical notes 166
4 J-contractive and J-inner matrix valued functions 169
4.1 The classes V{J) and U{J) 169
4.2 Blaschke-Potapov products 174
4.3 Entire J-inner mvf s 181
4.4 Multiplicative representations in the class V°(J) 185
4.5 The classes V(jpq) and U(jpq) 187
4.6 Associated pairs of the first kind 190
4.7 The classes V(JP), V(jp, Jp), U{JP) and U{jp, Jp) 195
4.8 Associated pairs of the second kind 198
4.9 Singular and regular J-inner mvf s 201
4.10 Domains of holomorphy of J inner mvf s 207
4.11 Growth constraints on J-inner mvf s 208
4.12 Monotonie sequences in V°(J) 209
4.13 Linear fractional transformations 211
4.14 Connections between the two kinds of associated pairs 217
4.15 Redheffer transforms 218
4.16 Strongly regular J-inner mvf s 219
4.17 Minus matrix valued functions 221
4.18 More on linear fractional transformations 230
4.19 Bibliographical notes 237
5 Reproducing kernel Hubert spaces 240
5.1 Preliminaries 240
5.2 Examples 247
Contents ix
5.3 A characterization of the spaces H(U) 254
5.4 A finite dimensional example and extensions thereof 261
5.5 Extension of H{U) into C for U G Vo(J) 266
5.6 The space H(b) for p x p inner mvf s b(X) 270
5.7 The space H*{b) for p x p inner mvf s b(A) 275
5.8 The space H(U) for m x m J-inner mvf s U(X) 276
5.9 The space H(W) for W € W(jpg) 289
5.10 The de Branges space ß(£) 293
5.11 Regular de Branges matrices Ê and spaces B{ £) 298
5.12 Connections between A and £ 300
5.13 A factorization and parametrization of mvf s A €U(JP). 302
5.14 A description of H(W) n Lf 308
5.15 Characterizations of the classes Us(J), Utr{J) and UrsR{J) 313
5.16 Regular J-inner mvf s 318
5.17 Formulas for W{ ) when W eUrsR(jpq) 318
5.18 A description of H{A) when A e UrsR{Jp) 322
5.19 Bibliographical notes 332
Operator nodes and passive systems 334
6.1 Characteristic mvf s of Livsic-Brodskii nodes 334
6.2 Connections with systems theory 348
6.3 Bibliographical notes 354
Generalized interpolation problems 358
7.1 The Nehari problem 359
7.2 7-generating matrices 364
7.3 Criteria for right regularity 381
7.4 Criteria for left regularity 390
7.5 Formulas for 21 when ||r|| 1 391
7.6 The generalized Schur interpolation problem 396
7.7 Generalized Sarason problems in SpXq and Hg* 401
7.8 Resolvent matrices for the GSP in the Schur class 404
7.9 The generalized Carathéodory interpolation problem 408
7.10 Connections between the GSIP and the GCIP 410
7.11 Generalized Sarason problems in Cpxp 413
7.12 Bibliographical notes 417
Generalized Krein extension problems 420
8.1 Helical extension problems 420
8.2 Positive definite extension problems 439
8.3 Positive definite and helical extension problems 441
8.4 Resolvent matrices for positive definite extension problems 443
x Contents
8.5 Tangential and bitangential positive extension problems 446
8.6 The Krein accelerant extension problem 449
8.7 The accelerant and helical extension problems 451
8.8 Conditions for strictly completely indeterminate HEP(g; a) 452
8.9 Formulas for the normalized resolvent matrix for the HEP 457
8.10 .B-resolvent matrices for the accelerant case 460
8.11 Bibliographical notes 467
9 Darlington representations and related inverse problems 470
9.1 ^-representations of mvf s seuil SpXq 471
9.2 Chain scattering ^-representations 481
9.3 P-representations in the class Cpxp 484
9.4 de Branges matrices and spectral functions 486
9.5 The inverse 12 block problem for jpç-inner mvf s 489
9.6 Inverse problems in special classes 490
9.7 Jp,r-inner Si-dilations of c 6 n O Cpxp 499
9.8 Rational approximation of mvf s of the class n D H^9 506
9.9 Bibliographical notes 512
10 More criteria for strong regularity 515
10.1 The matrix Muckenhoupt (A2) condition 515
10.2 Criteria of strong regularity for 7-generating matrices 518
10.3 Strong regularity for J-inner mvf s 521
10.4 A mvf U e £ D UTsR ( Jj ) that is not in Lfê2 525
10.5 Right and left strongly regular de Branges matrices 528
10.6 LB J-nodes with characteristic mvf s in Utsr (J) 531
10.7 Bibliographical notes 533
11 Formulas for entropy functionals 536
11.1 Definitions of the entropy functionals 536
11.2 Motivation for the terminology entropy functional 537
11.3 Entropy of completely indeterminate interpolation problems 538
11.4 Formulas for entropy functionals and their minimum 540
11.5 A matricial generalization of the entropy inequality 546
11.6 Bibliographical notes 549
Bibliography 551
Notation index 567
Subject index 571
|
| any_adam_object | 1 |
| author | Arov, Damir Z. 1934- |
| author_GND | (DE-588)172974356 (DE-588)124041205 |
| author_facet | Arov, Damir Z. 1934- |
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| author_sort | Arov, Damir Z. 1934- |
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| bvnumber | BV025517997 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV025517997 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:35:50Z |
| institution | BVB |
| isbn | 0521883008 9780521883009 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020126885 |
| oclc_num | 635569850 |
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| physical | XI, 575 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Arov, Damir Z. 1934- Verfasser (DE-588)172974356 aut J-contractive matrix valued functions and related topics Damir Z. Arov and Harry Dym 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2008 XI, 575 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 116 Matrixwertige Funktion (DE-588)4128928-6 gnd rswk-swf Matrixwertige Funktion (DE-588)4128928-6 s DE-604 Dym, Harry 1938- Sonstige (DE-588)124041205 oth Encyclopedia of mathematics and its applications 116 (DE-604)BV000903719 116 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020126885&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arov, Damir Z. 1934- J-contractive matrix valued functions and related topics Encyclopedia of mathematics and its applications Matrixwertige Funktion (DE-588)4128928-6 gnd |
| subject_GND | (DE-588)4128928-6 |
| title | J-contractive matrix valued functions and related topics |
| title_auth | J-contractive matrix valued functions and related topics |
| title_exact_search | J-contractive matrix valued functions and related topics |
| title_full | J-contractive matrix valued functions and related topics Damir Z. Arov and Harry Dym |
| title_fullStr | J-contractive matrix valued functions and related topics Damir Z. Arov and Harry Dym |
| title_full_unstemmed | J-contractive matrix valued functions and related topics Damir Z. Arov and Harry Dym |
| title_short | J-contractive matrix valued functions and related topics |
| title_sort | j contractive matrix valued functions and related topics |
| topic | Matrixwertige Funktion (DE-588)4128928-6 gnd |
| topic_facet | Matrixwertige Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020126885&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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