Contents

Chapters in this book

1. Frontmatter 1
2. Preface 5
3. Contents 7
4. List of Symbols 17
5. Introduction 19
6. Part I. Selfadjoint operators in Hilbert spaces
7. Introduction 25
8. 1. Preliminaries 26
9. 2. Multiplicity Theorie 41
10. 3. Spectral Theory 45
11. 4. Direct Integrals and Spectral Representations 67
12. 5. Operator Spectral Integrals 80
13. Notes and Remarks to Part I 93
14. Part II. Algebras of Asymptotic Constants
15. Introduction 95
16. 6. General Theory of Asymptotic Constants 97
17. 7. Special Classes of Asymptotic Constants 126
18. 8. The Invariance of Wave Morphisms and Wave Algebras 149
19. Notes and Remarks to Part II 167
20. Part III. Two-Space Wave Operators and Scattering Operators
21. Introduction 169
22. 9. Elementary Theory of Wave and Scattering Operators 170
23. 10. Identifikation Operators 195
24. 11. Structural Properties of Wave and Scattering Operators 233
25. 12. Lax-Phillips Evolutions and Two-Space Wave Operators 250
26. 13. Stationary Theory 264
27. Notes and Remarks to Part III 291
28. Part IV. Existence and Completeness of Wave Operators
29. Introduction 299
30. 14. Stationary methods 301
31. 15. Time-Falloff Methods 322
32. 16. Trace Class Methods 343
33. 17. Smooth Perturbations 356
34. Notes and Remarks to Part IV 374
35. Part V. Some Properties of the Scattering Operator, the Scattering Matrix, and the Scattering Amplitude
36. Introduction 381
37. 18. Representations of the Scattering Operator and the Scattering Amplitude, and Analyticity Properties of the Scattering Amplitude 382
38. 19. Spectral Properties of the Scattering Amplitude 400
39. Notes and Remarks to Part V 417
40. Bibliography 420
41. Subject Index 448