Topics in interpolation theory:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1997
|
| Schriftenreihe: | Operator theory
95 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 494 S. |
| ISBN: | 3764357231 0817657231 |
Internformat
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| 245 | 1 | 0 | |a Topics in interpolation theory |c ed. by H. Dym ... |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1997 | |
| 300 | |a XII, 494 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Operator theory |v 95 | |
| 650 | 7 | |a Interpolatie |2 gtt | |
| 650 | 7 | |a Operatortheorie |2 gtt | |
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Datensatz im Suchindex
| _version_ | 1804125742968078336 |
|---|---|
| adam_text | Table of contents
Welcoming remarks XIII
Editorial introduction XVII
Vladimir Petrovich Potapov, as remembered by colleagues,
friends and former students 1
M.S. Livsic 1
D.Z. Arov 8
L.A. Sakhnovich 12
A.A. Nudelrhah •.... : 13
V.K. pubovoj .... . :.., 14
V.E.Katsnelson , 16
N.I. Akhiezer
On a minimum problem in function theory and the number of
roots of an algebraic equation inside the unit disc 19
0. Introduction 19
1. An auxiliary result 20
2. The Caratheodory Fejer problem 23
3. A remark on Equation (14) 28
4. An application to the problem on the number of roots
of an algebraic equation in the disc 29
5. The G. Pick problem 31
References 34
D. Alpay and V. Bolotnikov
On tangential interpolation in reproducing kernel Hilbert
modules and applications 37
1. Introduction 37
2. Reproducing kernel Hilbert modules 39
3. The left sided Nevanlinna Pick problem 43
4. The left sided Caratheodory Fejer problem 46
5. Right sided interpolation^ 49
6. On the recursive solution and the solvability criterion 52
7. The case of Hardy spaces 54
8. An example: interpolation in Hardy Sobolev spaces 54
VI Table of contents
9. Interpolation in Dirichlet spaces 58
10. Interpolation in Bergman spaces 59
11. Some remarks on interpolation in de Branges Rovnyak spaces 60
References 65
A. Dijksma and H. hanger
Notes on a Nevanlinna Pick interpolation problem for
generalized Nevanlinna functions 69
1. Introduction 69
2. The model 72
3. Selfadjoint extensions of the model and the solutions
of the interpolation problem 77
4. A parametrization 79
5. Excluded parameters 84
References 89
V.K. Dubovoj
The indefinite metric in the Schur interpolation problem
for analytic functions, IV 93
10. Solving the degenerate Schur problem 93
References 103
H. Dym and B. Freydin
Bitangential interpolation for upper triangular operators 105
1. Introduction 105
2. The basic interpolation problem 110
3. The augmented BIP 115
4. Coupling 125
5. Linear fractional representation of all solutions 132
6. Formulas for the standard unitary colligation A 137
References 141
H. Dym and B. Freydin
Bitangential interpolation for upper triangular operators when
the Pick operator is strictly positive 143
7. Strictly positive Pick operators 143
8. Chain scattering operators 150
9. The maximum entropy problem 157
10. Positive real interpolants 159
References 163
Table of contents VII
Yu.M. Dyukarev
Integral representations of a pair of nonnegative operators and
interpolation problems in the Stieltjes class 165
1. Introduction 165
2. The formulation of the problem about consistent representation
of the pair of nonnegative operators 166
3. The system of fundamental matrix inequalities of V.P. Potapov 168
4. The transformation of the FMI of V.P. Potapov 171
5. J expansive functions associated with a nondegenerate
system of FMFs 177
6. The solution of the FMI system in the nondegenerate case 181
References 183
Yu.P. Ginzburg
On recovering a multiplicative integral from its modulus 185
0. Preface 185
1. On one factorization of an absolutely continuous
operator function 186
2. The modulus of the multiplicative integral of a
Hermitian valued function 187
3. On some classes of analytic operator functions and their
multiplicative representations 188
References 193
L. Golinskii
On Schur functions and Szego orthogonal polynomials 195
References 203
L. Golinskii and I. Mikhailova
Hilbert spaces of entire functions as a J theory subject 205
0. Preface 205
1. Preliminaries from J theory 206
2. de Branges matrices 212
3. Parametrization of de Branges matrices 220
4. de Branges spaces 226
5. Structure of perfect de Branges matrices and basic formulas 229
6. Parseval s equality 235
References 251
VIII Table of contents
V.E. Katsnelson
On transformations of Potapov s fundamental matrix inequality 253
0. Preface 253
1. The FMI and its structure 254
2. The FMI for the Nevanlinna Pick problem 256
3. Derivation of the FMI (AfV) 257
4. The Hamburger moment problem as a classical
interpolation problem 260
5. Derivation of the FMI {H) 263
6. Transformation of the FMI (H) 265
7. On using the TFMI (H) to obtain interpolation information
from the FMI (H) 269
8. Transformation of the FMI (MV) 274
References 280
V.E. Katsnelson, A.Ya. Kheifets and P.M. Yuditskii
An abstract interpolation problem and the extension theory
of isometric operators 283
1. Interpolation data and examples 283
2. V.P. Potapov s fundamental matrix inequality
and its transformation 285
3. The abstract interpolation problem 295
References 297
V.E. Katsnelson and B. Kirstein
On the theory of matrix valued functions belonging
to the Smirnov class 299
0. Preface 300
1. On the matricial Nevanlinna and Smirnov classes 302
2. Matrix functions of the Smirnov class as multiples of
contractive matrix functions 307
3. Outer matrix valued functions 310
4. Matrix valued inner functions 319
5. Inner outer factorization 323
6. An analogue of Frostman s theorem for matrix functions
of the Smirnov class 330
References 341
Table of contents IX
/. V. Kovalishina
Integral representation of function of class ICa 351
1. Formulation of the problem 351
2. The fundamental matrix inequality (FMI) 353
3. The unification of the FMI and the Sakhnovich identity 355
4. The case of more than one representation 356
References 359
M.G. Krein
On the theory of entire matrix functions of exponential type 361
0. Introduction 361
1. Proof of the main theorem 362
2. Applications of the theorem for the investigation
of a monodromy matrix 364
3. On a special case of the system (2.1) 368
References 371
S. Kupin and P. Yuditskii
Analogs of Nehari and Sarason theorems for character automorphic functions
and some related questions 373
0. Introduction 373
1. Groups of Widom Carleson type and Hardy spaces of
character automorphic functions 374
2. Character automorphic analogs of the Nehari
and Sarason Theorems 378
3. A solvability criterion for the character automorphic
Nevanlinna Pick problem and the uniqueness of solution 381
4. A solvability criterion for the Nevanlinna Pick problem in
the plane with a homogeneous compact removed 385
References 390
M.S. Livsic
The Blaschke Potapov factorization theorem and the theory
of nonselfadjoint operators 391
0. Preface 391
1. Characteristic functions 392
2. Potapov s factorization theorem 395
References 396
X Table of contents
I. V. Mikhailova
Weyl matrix circles as a tool for uniqueness in the theory
of multiplicative representation of J inner functions 397
References 416
/. V. Mikhailova and V.P. Potapov
On a criterion of positive definiteness 419
0. Introduction 419
1. The triad 421
2. The value A(£) 423
3. The fundamental antilinear forms £?(/), Lf (/), C4(/) 427
4. The matrix function W(z, £) and the related canonical system 431
5. The relationship between the matrix function W(z, £)
and the original problem 437
6. The formulation of the Main Theorem 446
7. The discussion of the Main Theorem 447
8. An example 449
References 450
E. Russakovskii
Matrix boundary value problems with eigenvalue dependent
boundary conditions (The linear case) 453
0. Introduction 453
1. Notation and remarks 454
2. The operator T in the space C2d(0,1) 455
3. The generalized Lagrange identity for the operator T 456
4. The appropriate indefinite scalar product in the
Pontryagin space £^(0,1) 457
5. Properties of the operator T 457
6. Comparison with earlier results 458
References 460
Table of contents XI
L.A. Sakhnovich
Weyl Titchmarsh functions of the canonical periodical system
of differential equations 463
0. Introduction 463
1. On multipliers 464
2. Weyl Titchmarsh functions 466
3. Singular points of the Weyl matrix function 469
4. Transformation of the Weyl Titchmarsh function 477
References 478
V.I. Smirnov
On boundary values of functions regular in a disk 481
References 494
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| language | English |
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| spelling | Topics in interpolation theory ed. by H. Dym ... Basel [u.a.] Birkhäuser 1997 XII, 494 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 95 Interpolatie gtt Operatortheorie gtt Interpolation Interpolation (DE-588)4162121-9 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Interpolation (DE-588)4162121-9 s DE-604 Dym, Harry 1938- Sonstige (DE-588)124041205 oth Operator theory 95 (DE-604)BV000000970 95 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007544990&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4162121-9 (DE-588)4143413-4 |
| title | Topics in interpolation theory |
| title_auth | Topics in interpolation theory |
| title_exact_search | Topics in interpolation theory |
| title_full | Topics in interpolation theory ed. by H. Dym ... |
| title_fullStr | Topics in interpolation theory ed. by H. Dym ... |
| title_full_unstemmed | Topics in interpolation theory ed. by H. Dym ... |
| title_short | Topics in interpolation theory |
| title_sort | topics in interpolation theory |
| topic | Interpolatie gtt Operatortheorie gtt Interpolation Interpolation (DE-588)4162121-9 gnd |
| topic_facet | Interpolatie Operatortheorie Interpolation Aufsatzsammlung |
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