Realizability Theory for Continuous Linear Systems
Published on 14. May 2014
249 pages
978-0-08-095606-0 (ISBN)
Description
Realizability Theory for Continuous Linear Systems
More details
Series
Language
English
Place of publication
San Diego
United States
ISBN-13
978-0-08-095606-0 (9780080956060)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
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A. H. Zemanian
Realizability Theory for Continuous Linear Systems
Book
01/1972
Academic Press
€68.09
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Content
- 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
