Contents
Preface
Acknowledgments
1 Introduction
1.1 Function-Theoretic Operator Theory on Vectorial Hardy Spaces, Reproducing Kernel Hilbert Spaces, and Discrete-Time Linear Systems: Background
1.2 The Synthesis of the Systems-Theory and Reproducing Kernel Approaches
1.3 StandardWeighted Bergman Spaces
1.4 The Hardy–Fock Space Setting
1.5 Weighted Bergman–Fock Spaces
1.6 Overview
1.7 Notes
2 Formal Reproducing Kernel Hilbert Spaces
2.1 Basic Definitions
2.2 Weighted Hardy–Fock Spaces
2.3 Notes
3 Contractive Multipliers
3.1 Contractive Multipliers in General
3.2 Contractive Multipliers between Hardy-Fock Spaces
3.3 A Noncommutative Leech's Theorem
3.4 Contractive Multipliers from H2U (F + d ) to H2 ω,Y(F + d ) for Admissible ω
3.5 H2 ω,Y(F + d )-Bergman-Inner Formal Power Series
3.6 Notes
4 Stein Relations and Observability Range Spaces
4.1 Preliminaries on Functional Calculus for the Operator BA
4.2 Observability, Defect and Shifted Defect Operators
4.3 Shifted Observability Operators and Observability Gramians
4.4 The Model Shift-Operator Tuple on H^2_ω y (F^+d)
4.5 A Wold Decomposition for ω-Isometric-like Operator Tuples
4.6 Observability-Operator Range Spaces
4.7 Notes
5 Beurling Lax Theorems Based on Contractive Multipliers
5.1 Beurling–Lax Representations with Model Space H2U (F^+_d)
5.2 Beurling-Lax Representations Based on Contractive Multipliers from H^2{ω',U}(F^+d) to H^2{ω,y}(F^+d)
5.3 Representations with Model Space of the Form \oplus ^n{j=1} A_{j,U_j} (F^+d)
5.4 Notes
6 Non orthogonal Beurling Lax Representations Based on Wandering Subspaces
6.1 Beurling–Lax Quasi-Wandering Subspace Representations
6.2 Non-orthogonal Beurling–Lax Representations Based on Wandering Subspaces
6.3 Notes
7 Orthogonal Beurling Lax Representations Based on Wandering Subspaces
7.1 Transfer Functions θ{ω,U_β} and Metric Constraints
7.2 Beurling–Lax Representations Based on Bergman-Inner Families
7.3 Expansive Multiplier Property
7.4 Bergman-Inner Multipliers as Extremal Solutions of Interpolation Problems
7.5 Notes
8 Models for ω-Hypercontractive Operator Tuples
8.1 Model Theory Based on Observability Operators
8.2 The Characteristic Function Approach
8.3 Model Theory for n-Hypercontractions
8.4 Notes
9 Weighted Hardy Fock Spaces Built from a Regular Formal Power Series
9.1 Preliminaries
9.2 The Spaces H^2_{ ω_{p,n},Y}(F^+d) and Their Contractive Multipliers
9.3 Output Stability, Stein Equations, and Inequalities
9.4 The ω{p,n}, -Shift Model Operator Tuple S_{ω_{p,n},R}
9.5 Observability Operator Range Spaces in H^2_{ω_{p,n},y}(F^+_d)
9.6 Beurling-Lax Theorems Based on Contractive Multipliers
9.7 Beurling-Lax Representations via Quasi-Wandering Subspaces
9.8 Beurling-Lax Representations Based on Bergman-Inner Families
9.9 Operator Model Theory for c.n.c. ∗-(p,n)-Hypercontractive Tuples
9.10 Notes
References
[15]
[32]
[46]
[63]
[82]
[101]
[119]
[140]
[162]
Notation Index
Subject Index