Linear differential equations and functions spaces

Linear Differential Equations and Function Spaces......Page 4
Copyright Page......Page 5
Contents......Page 16
Preface......Page 8
PART I......Page 22
10. Introduction......Page 24
11. Angles, splittings, and dihedra......Page 28
12. Coupled spaces......Page 34
13. The class of subspaces of a Banach space......Page 39
14. Hilbert space......Page 47
15. Notes to Chapter 1......Page 52
20. Introduction......Page 54
21. N-spaces......Page 62
22. F-spaces......Page 67
23. F-spaces......Page 78
24. Spaces of continuous functions......Page 97
25. Notes to Chapter 2......Page 104
30. Introduction......Page 105
31. Solutions......Page 107
32. Associate equations in coupled spaces......Page 110
33. D-solutions of homogeneous equations......Page 113
34. Notes to Chapter 3......Page 118
PART II......Page 120
40. Introduction......Page 122
41. Ordinary dichotomies......Page 123
42. Exponential dichotomies......Page 131
43. Dichotomies for associate equations......Page 138
44. Finite-dimensional space......Page 141
45. Notes to Chapter 4......Page 143
50. Introduction......Page 145
51. Admissibility......Page 147
52. (B, D)-manifolds......Page 159
53. (B, D)-manifolds, admissibility, and the associate equations......Page 170
54. (B, D)-subspaces and the associate equations......Page 176
55. Finite-dimensional space......Page 181
56. Notes to Chapter 5......Page 183
60. Introduction......Page 186
61. The fundamental inequalities......Page 188
62. Predichotomy behavior of the solutions of the homogeneous equation......Page 191
63. Admissibility, (B, D)-subspaces, and dichotomies: the general case......Page 200
64. Admissibility, (B, D)-subspaces, and dichotomies: the equation with A ε M(X)......Page 209
65. Examples and comments......Page 213
66. Behavior of the solutions of the associate homogeneous equation......Page 232
67. Notes to Chapter 6......Page 242
70. Introduction......Page 244
71. Admissibility classes and (B, D)-subspaces......Page 245
72. Dichotomy classes......Page 258
73. Connection in dichotomy classes: Banach spaces......Page 266
74. Connection in dichotomy classes: Hilbert space......Page 272
75. Notes to Chapter 7......Page 290
80. Introduction......Page 292
81. (B, D)-dihedra and admissibility......Page 294
82. Double dichotomies. Connections with admissibility and (B, D)-dihedra......Page 300
83. Associate equations......Page 314
84. Dependence on A......Page 317
PART III......Page 330
90. Introduction......Page 332
91. Ljapunov functions......Page 337
92. Exponential dichotomies......Page 341
93. Ordinary dichotomies......Page 348
94. Notes to Chapter 9......Page 353
100. Introduction......Page 354
101. The condition Xo*a = {0}......Page 359
102. Exponential dichotomies......Page 362
103. Reflexive and finite-dimensional spaces......Page 364
104. Notes to Chapter 10......Page 366
110. Introduction......Page 369
111. Floquet representation......Page 372
112. Periodic equations and periodic solutions......Page 375
113. The solutions of the homogeneous equation......Page 379
114. Individual periodic equations......Page 390
120. Introduction......Page 394
121. The (m + 1)st-order equation......Page 397
122. Admissibility and (B, D)-manifolds......Page 402
123. The main theorems......Page 407
References......Page 414
Index Author and subject......Page 420
Notation......Page 423