Linear Systems and Operators in Hilbert Space

by Paul A. Fuhrmann

Overview

A treatment of system theory within the context of finite dimensional spaces, this text is appropriate for students with no previous experience of operator theory. The three-part approach, with notes and references for each section, covers linear algebra and finite dimensional systems, operators in Hilbert space, and linear systems in Hilbert space. 1981 edition.

Product Details

ISBN-13:	9780486782263
Publisher:	Dover Publications
Publication date:	12/17/2013
Series:	Dover Books on Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	336
File size:	27 MB
Note:	This product may take a few minutes to download.

About the Author

Paul A. Fuhrmann is Professor of Mathematics at Ben-Gurion University of the Negev in Beer-Sheva, Israel.

Table of Contents

Chapter I Linear algebra and finite dimensional systems 1

Introduction 1

1 Rings and modules 2

2 Polynomial modules 6

3 The Smith canonical form 12

4 Structure of linear transformations 15

5 Linear systems 28

6 Reachability, observability, and realizations 31

7 Hankel matrices 32

8 Simulation and isomorphism 34

9 Transfer functions and their factorizations 38

10 Realization theory 39

11 Polynomial system matrices 43

12 Generalized resultant theorem 46

13 Feedback 50

Notes and references 62

Chapter II Operators in Hilbert space 63

1 Geometry of Hilbert space 63

2 Bounded operators in Hilbert space 70

3 Unbounded operators 77

4 Representation theorems 83

5 The spectral theorem 93

6 Spectral representations 104

7 The Douglas factorization theorem and related results 124

8 Shifts, isometries, and the Wold decomposition 126

9 Contractions, dilations, and models 129

10 Semigroups of operators 140

11 The lifting theorem 161

12 Elements of H² theory 167

13 Models for contractions and their spectra 190

14 The functional calculus for contractions 197

15 Jordan models 208

Notes and references 236

Chapter III Linear systems in Hubert space 239

1 Fundamental concepts 239

2 Hankel operators and realization theory 248

3 Restricted shift systems 251

4 Spectral minimality of restricted shift systems 259

5 Degree theory for strictly noncyclic functions 268

6 Continuous time systems 289

7 Symmetric systems 307

Notes and references 317

References 318

Index 323