Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Formal Reproducing Kernel Hilbert Spaces
- 3 Contractive Multipliers
- 4 Stein Relations and Observability Range Spaces
- 5 Beurling–Lax Theorems Based on Contractive Multipliers
- 6 Non-orthogonal Beurling–Lax Representations Based on Wandering Subspaces
- 7 Orthogonal Beurling–Lax Representations Based on Wandering Subspaces
- 8 Models for ω-Hypercontractive Operator Tuples
- 9 Weighted Hardy–Fock Spaces Built from a Regular Formal Power Series
- References
- Notation Index
- Subject Index
7 - Orthogonal Beurling–Lax Representations Based on Wandering Subspaces
Published online by Cambridge University Press: 09 December 2021
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Formal Reproducing Kernel Hilbert Spaces
- 3 Contractive Multipliers
- 4 Stein Relations and Observability Range Spaces
- 5 Beurling–Lax Theorems Based on Contractive Multipliers
- 6 Non-orthogonal Beurling–Lax Representations Based on Wandering Subspaces
- 7 Orthogonal Beurling–Lax Representations Based on Wandering Subspaces
- 8 Models for ω-Hypercontractive Operator Tuples
- 9 Weighted Hardy–Fock Spaces Built from a Regular Formal Power Series
- References
- Notation Index
- Subject Index
Summary
Chapter 7 obtains a Beurling–Lax representation for an isometrically included forward-shift-invariant subspace of a weighted Hardy–Fock space which involves a whole family of Bergman-inner-like multipliers (rather than a single inner multiplier) which leads to an orthogonal decomposition of the forward-shift-invariant subspace. The Bergman-inner family can be viewed as the transfer-function family for a time-varying noncommutative, multidimensional weighted-conservative input/state/output linear system, and can be viewed as a time-varying isometric multiplier from a time-varying unweighted Hardy–Fock space to the given weighted Hardy–Fock space.
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- Publisher: Cambridge University PressPrint publication year: 2021