Linear Systems and Operators in Hilbert Space

Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Contents......Page 4
Introduction......Page 8
1. Rings and modules......Page 9
2. Polynomial modules......Page 13
3. The Smith canonical form......Page 19
4. Structure of linear transformations......Page 22
5. Linear systems......Page 35
6. Reachability, observability, and realizations......Page 38
7. Hankel matrices......Page 39
8. Simulation and isomorphism......Page 41
9. Transfer functions and their factorizations......Page 45
10. Realization theory......Page 46
11. Polynomial system matrices......Page 50
12. Generalized resultant theorem......Page 53
13. Feedback......Page 57
Notes and references......Page 69
1 . Geometry of Hilbert space......Page 70
2. Bounded operators in Hilbert space......Page 77
3. Unbounded operators......Page 84
4. Representation theorems......Page 90
5. The spectral theorem......Page 100
6. Spectral representations......Page 111
7. The Douglas factorization theorem and related results......Page 131
8. Shifts, isometries, and the Wold decomposition......Page 133
9. Contractions, dilations, and models......Page 136
10. Semigroups of operators......Page 147
11. The lifting theorem......Page 168
12. Elements of H^2 theory......Page 174
13. Models for contractions and their spectra......Page 197
14. The functional calculus for contractions......Page 204
15. Jordan models......Page 215
Notes and references......Page 243
1. Fundamental concepts......Page 246
2. Hankel operators and realization theory......Page 255
3. Restricted shift systems......Page 258
4. Spectral minimality of restricted shift systems......Page 266
5. Degree theory for strictly noncyclic functions......Page 275
6. Continuous time systems......Page 296
7. Symmetric systems......Page 314
Notes and references......Page 324
References......Page 325
Index......Page 330
Back Cover......Page 333