Linear Differential Equations and Function Spaces (Pure and Applied Mathematics)

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 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. 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