| TABLE OF CONTENTS
REALIZABILITY THEORY FOR CONTINUOUS LINEAR SYSTEMS |
| TABLE OF CONTENTS Preface Chapter 1. Vector-Valued Functions 1.1 Introduction 1.2 Notations and Terminology 1.3 Continuous Functions 1.4 Integration 1.5 Repeated Integration and Improper Integrals 1.6 Differentiation 1.7 Banach-Space-Valued Analytic Functions 1.8 Contour Integration Chapter 2. Integration with Vector-Valued Functions and Operator-Valued Measures 2.1 Introduction 2.2 Operator-Valued Measures 2.3 sigma-Finite Operator-Valued Measures 2.4 Tensor Products and Vector-Valued Functions 2.5 Integration of Vector-Valued Functions 2.6 Sesquilinear Forms Generated by PO Measures Chapter 3. Banach-Space-Valued Testing Functions and Distributions 3.1 Introduction 3.2 The Basic Testing-Function Space 3.3 Distributions 3.4 Local Structure 3.5 A Correspondence between Banach-Space-Valued Operators 3.6 The rho-Type Testing Function Spaces 3.7 Generalized Functions 3.8 L_p Type Testing Functions and Distributions Chapter 4. Kernel Operators 4.1 Introduction 4.2 Systems and Operators 4.3 A Testing-Function Space 4.4 The Kernel Theorem 4.5 Kernel Operators 4.6 Causality and Kernel Operators Chapter 5. Convolution Operators 5.1 Introduction 5.2 Convolution 5.3 Special Cases 5.4 The Commutativity of Convolution with Shifting and Differentiation 5.5 Regularization 5.6 Primitives 5.7 Direct Products 5.8 Distribution That Are Independent of Certain Coordinates 5.9 A Change-of-Variable Formula 5.10 Convolution Operators 5.11 Causality and Convolution Operators Chapter 6. The Laplace Transformation 6.1 Introduction 6.2 The Definition of the Laplace Transformation 6.3 Analyticity and the Exchange Formula 6.4 Inversion and Uniqueness 6.5 A Causality Criterion Chapter 7. The Scattering Formulism 7.1 Introduction 7.2 Preliminary Consideration Concerning Integrable Distributions 7.3 Scatter Passivity 7.4 Bounded* Scattering Transforms 7.5 The Realizability of Bounded* Scattering Transforms 7.6 Bounded*-Real Scattering Transforms 7.7 Lossless Hilbert Ports 7.8 The Lossless Hilbert n-Port Chapter 8. The Admittance Formulism 8.1 Introduction 8.2 Passivity 8.3 Linearity and Semipassivity Imply Continuity 8.4 The Fourier Transformation on Distributions of Slow Growth 8.5 Local Mappings 8.6 Positive Sesquilinear Forms 8.7 Positive Sesquilinear Forms on Hilbert-Space-Valued Functions 8.8 Certain Semipassive Mappings 8.9 An Extension of the Bochner-Schwartz Theorem 8.10 Representations of Certain Causal Semipassive Mappings 8.11 A Representation for Positive* Transforms 8.12 Positive* Admittance Transforms 8.13 Positive* Real Admittance Transforms 8.14 A Connection between Passivity and Semipassivity 8.15 A Connection between the Admittance and Scattering Formulisms 8.16 The Admittance Transform of a Lossless Hilbert Port Appendix A. Linear Spaces Appendix B. Topological Spaces Appendix C. Topological Linear Spaces Appendix D. Continuous Linear Mappings Appendix E. Inductive-Limit Spaces Appendix F. Bilinear Mappings and Tensor Products Appendix G. The Bochner Integral Bibliography Index of Symbols Index |
