Linear Differential Equations and Function Spaces
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Contents
Preface
PART I
Chapter 1. Geometry of Banach spaces
10. Introduction
11. Angles, splittings, and dihedra
12. Coupled spaces
13. The class of subspaces of a Banach space
14. Hilbert space
15. Notes to Chapter 1
Chapter 2. Function spaces
20. Introduction
21. N-spaces
22. F-spaces
23. F-spaces
24. Spaces of continuous functions
25. Notes to Chapter 2
Chapter 3. Linear differential equations
30. Introduction
31. Solutions
32. Associate equations in coupled spaces
33. D-solutions of homogeneous equations
34. Notes to Chapter 3
PART II
Chapter 4. Dichotomies
40. Introduction
41. Ordinary dichotomies
42. Exponential dichotomies
43. Dichotomies for associate equations
44. Finite-dimensional space
45. Notes to Chapter 4
Chapter 5. Admissibility and related concepts
50. Introduction
51. Admissibility
52. (B, D)-manifolds
53. (B, D)-manifolds, admissibility, and the associate equations
54. (B, D)-subspaces and the associate equations
55. Finite-dimensional space
56. Notes to Chapter 5
Chapter 6. Admissibility and dichotomies
60. Introduction
61. The fundamental inequalities
62. Predichotomy behavior of the solutions of the homogeneous equation
63. Admissibility, (B, D)-subspaces, and dichotomies: the general case
64. Admissibility, (B, D)-subspaces, and dichotomies: the equation with A ε M(X)
65. Examples and comments
66. Behavior of the solutions of the associate homogeneous equation
67. Notes to Chapter 6
Chapter 7. Dependence on A
70. Introduction
71. Admissibility classes and (B, D)-subspaces
72. Dichotomy classes
73. Connection in dichotomy classes: Banach spaces
74. Connection in dichotomy classes: Hilbert space
75. Notes to Chapter 7
Chapter 8. Equations on R
80. Introduction
81. (B, D)-dihedra and admissibility
82. Double dichotomies. Connections with admissibility and (B, D)-dihedra
83. Associate equations
84. Dependence on A
PART III
Chapter 9. Ljapunovโs method
90. Introduction
91. Ljapunov functions
92. Exponential dichotomies
93. Ordinary dichotomies
94. Notes to Chapter 9
Chapter 10. Equations with almost periodic A
100. Introduction
101. The condition Xo*a = {0}
102. Exponential dichotomies
103. Reflexive and finite-dimensional spaces
104. Notes to Chapter 10
Chapter 11. Equations with periodic A
110. Introduction
111. Floquet representation
112. Periodic equations and periodic solutions
113. The solutions of the homogeneous equation
114. Individual periodic equations
Chapter 12. Higher-order equations
120. Introduction
121. The (m + 1)st-order equation
122. Admissibility and (B, D)-manifolds
123. The main theorems
References
Index Author and subject
Notation