UID:
almahu_9947366705602882
Format:
1 online resource (425 pages)
ISBN:
1-281-76636-4
,
9786611766368
,
0-08-087333-2
Series Statement:
Pure and applied mathematics : a series of monographs and textbooks ; v. 21
Content:
Linear differential equations and function spaces
Note:
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
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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
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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
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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
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Chapter 11. Equations with periodic A110. 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
,
English
Additional Edition:
ISBN 0-12-374568-3
Language:
English
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