Linear Differential Equations and Function Spaces
Linear Differential Equations and Function Spaces
Academic Press
Published on 29. August 2011
401 pages
978-0-08-087333-6 (ISBN)
Description
Linear Differential Equations and Function Spaces
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Content
- Front Cover
- Linear Differential Equations and Function Spaces
- Copyright Page
- 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 e 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. Ljapunov's 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
