Operator theory and interpolation, IWOTA 96 9783034895606, 9783034884228, 1991179200, 1964115256, 1989842860, 1983518522, 1994117184, 1992122210

Table of contents :
Title Page......Page 3
Copyright Page......Page 4
Contents......Page 5
Editorial Preface......Page 7
Classical Nevanlinna-Pick Interpolation with Real Interpolation Points......Page 8
Introduction......Page 8
1 Existence of Solutions and the Model......Page 12
2 Characterization of the Solutions by Selfadjoint Extensions......Page 17
3 The Defect Numbers of S, Canonical Extensions......Page 20
4 Uniqueness and Nonuniqueness of Solutions I......Page 24
5 Parametrization of Solutions......Page 26
6 Existence of a Solution and Reproducing Kernels......Page 35
7 Uniqueness and Nonuniqueness of Solutions II......Page 41
8 Examples......Page 49
9 Appendix: Nevanlinna Functions......Page 50
References......Page 55
The Abstract Interpolation Problem and Commutant Lifting: A Coordinate-free Approach......Page 58
Introduction......Page 58
1 The Abstract Interpolation Problem: Statementand Main Result......Page 60
2 Unitary Colligations and Abstract Scattering Systems......Page 65
3 Main Theorem on Coordinate-free AbsractInterpolation Problem......Page 75
4 The Commutant Lifting Theorem in Coordinate-free Form......Page 79
References......Page 88
On Classes of Realizable Operator-valued R-functions......Page 91
1 Introduction......Page 91
2 Preliminaries......Page 92
3 Linear Stationary Conservative Dynamic Systems......Page 102
Acknowledgement......Page 116
References......Page 116
......Page 119
1 Introduction......Page 119
2 Preliminaries......Page 120
2.1 Derivations or 1-cocycles......Page 120
2.2 Ext lOver the Polydisk Algebra......Page 121
3 Submodules L 2JI'N......Page 122
4 Hankel Operators......Page 126
References......Page 127
Kolmogorov Decompositions and the Realization of Time Dependent Systems......Page 129
1 Introduction......Page 129
2 Realization of Lower Triangular Families......Page 132
3 Applications......Page 137
References......Page 149
Hankel Forms and Operators in Hardy Spaces with Two Szego Weights......Page 151
Introduction......Page 151
1 Notation and Basic Result......Page 152
2 Szego easures and Model Subspaces......Page 154
3 Hankel Forms and Carleson Measures in B 2 .......Page 158
4 Generalizations for Pairs of Szego Weights......Page 164
References......Page 168
The Structured Norm of a Hilbert Space Operator with respect to a Given Algebra of Operators......Page 169
1 Introduction......Page 169
2 Preliminaries......Page 171
......Page 171
4 Finding JlDmA for R = C......Page 178
References......Page 188
Order Preserving Operator Function via Furuta Inequality A B 0 Ensures......Page 190
1 Introduction......Page 191
2 Results......Page 193
3 Proofs of results......Page 194
References......Page 199
On a Nonlinear Causal Commutant Lifting Theorem*......Page 200
1 Introduction......Page 200
2 Causal Analytic Mappings......Page 201
3 Nonlinear Causal Commutant Lifting Theorem......Page 204
4 Nonlinear Causal Hankel Mappings......Page 210
5 Nonlinear Interpolation and Robust Control......Page 214
References......Page 216
Parametrization of Solutions of the Nehari Problem and Nonorthogonal Dynamics......Page 218
Introduction......Page 218
1 Setting of the Nehari Problem......Page 218
2 Associated Isometry......Page 219
3 Unitary Extensions of V and All......Page 220
4 Motivation of the Definition of the Scattering Function......Page 225
5 Structure of Minimal Unitary Extensions of the Isometry V......Page 226
6 Scattering Function of the Colligation Ao motivation......Page 228
7 Scattering Function of the Colligation Ao formulas......Page 230
On Zeros of Defining Functions for some Hilbert Spaces of Polynomials......Page 239
1 Introduction......Page 239
2 Properties of Hypergeometric Series......Page 240
3 Proof of Theorem 1......Page 242
4 A Second Proof of Theorem 4......Page 245
References......Page 247
One or 1o Parameter Algebraic Scattering Systems and the Commutant Lifting Theorem......Page 248
1 Introduction......Page 248
2 Description of ..ext......Page 250
3 Commutant Lifting Theorem......Page 250
4 Unitary c-commuting Extension of a Pair of Isometries......Page 252
5 Two-parameter Algebraic Scattering System......Page 253
6 Description of ..ext xt for a Two-parameterAlgebraic Scattering System......Page 254
References......Page 256
On Interpolation Problems in the Complex Right Half Plane......Page 257
1 Introduction......Page 257
......Page 258
3 Proofs......Page 260
4 Some State Space Formulas......Page 264
5 Example......Page 267
Acknowledgements......Page 267
References......Page 268
Maximum Entropy Truncable Positive Definite Sequences of Analytic Toeplitz Operators*......Page 270
1 Preliminaries......Page 270
2 Sequences of Analytic Toeplitz Operators......Page 272
......Page 275
4 Maximum Entropy Truncable Sequences......Page 284
......Page 294
References......Page 296
Subdecomposable Operators and Rationally Invariant Subspaces......Page 298
1 Introduction......Page 298
2 A Matrix Model for Decomposable Operators......Page 299
3 Rationally Invariant Subspaces......Page 304
4 Pure Cyclic Hyponormal Operators......Page 308
References......Page 309