Contents
A Few Words about the Book v
Part C. Model Operators and Free Interpolation 1
Foreword to Part C 5
Chapter 1. The Basic Function Model 9
1.1. Unitary Dilations 9
1.2. Functional Embeddings and the Characteristic Function 17
1.3. The Function Model and Its Transcriptions 28
1.4. Models for Certain Accretive and Dissipative Operators 35
1.5. Exercises and Further Results 43
1.6. Notes and Remarks 73
Chapter 2. Elements of Spectral Theory in the Language of the Characteristic
Function 87
2.1. Invariant Subspaces 87
2.2. The H°° Functional Calculus 97
2.3. The Class Co, Minimal Annihilators, and the Spectrum of MQ 100
2.4. The Commutant Lifting Theorem 104
2.5. Exercises and Further Results 106
2.6. Notes and Remarks 137
Chapter 3. Decompositions into Invariant Subspaces and Free Interpolation 153
3.1. Unconditional Bases 155
3.2. Generalized Free Interpolation 160
3.3. Exercises and Further Results 170
3.4. Notes and Remarks 191
Part D. Analytic Problems in Linear System Theory 197
Foreword to Part D 201
Chapter 1. Basic Theory 205
1.1. The Main Formula 205
1.2. Initial Observations about Controllability 205
1.3. Basic Criteria for ACO, ECO, and NCO 207
1.4. Stable Systems 218
1.5. An Example: Heating of a Metal Bar 220
1.6. Exercises and Further Results 222
1.7. Notes and Remarks 233
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