Realizability Theory for Continuous Linear Systems

Name: Realizability Theory for Continuous Linear Systems
Brand: Academic Press
Price: 71.95 EUR
Availability: OnlineOnly

Zemanian(Autor*in)

Zemanian(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

249 Seiten

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978-0-08-095606-0 (ISBN)

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Front Cover
Realizability Theory for Continuous Linear Systems
Copyright Page
Contents
Preface
Acknowledgments
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 lntroduction
2.2 Operator-Valued Measures
2.3 s-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 Dm(A)
3.3 Distributions
3.4 Local Structure
3.5 The Correspondence between [D(A)
B] and [D
[ A
B]]
3.6 The ?-Type Testing Function Spaces
3.7 Generalized Functions
3.8 Lp-Type Testing Functions and Distributions
Chapter 4. Kernel Operators
4.1 Introduction
4.2 Systems and Operators
4.3 The Space H = D(V)
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 Operators with Shifting and Differentiation
5.5 Regularization
5.6 Primitives
5.7 Direct Products
5.8 Distributions That Are Independent of Certain Coordinates
5.9 A Change-of-Variable Formua
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 Considerations Concerning Lp-Type 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 J(H)
8.5 Local Mappings
8.6 Positive Sesquilinear Forms on D × D
8.7 Positive Sesquilinear Forms on D(H) × D(H)
8.8 Certain Semipassive Mappings of D(H) into E(H)
8.9 An Extension of the Bochner-Schwartz Theorem
8.10 Representations for 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
References
Index of Symbols
Index

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