Linear differential equations and function spaces:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Acad. Pr.
1967
|
| Ausgabe: | 2. print. |
| Schriftenreihe: | Pure and applied mathematics
21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 404 S. |
Internformat
MARC
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| 100 | 1 | |a Massera, José L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear differential equations and function spaces |c José Luis Massera ; Juan Jorge Schäffer |
| 250 | |a 2. print. | ||
| 264 | 1 | |a New York u.a. |b Acad. Pr. |c 1967 | |
| 300 | |a XX, 404 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied mathematics |v 21 | |
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| 650 | 0 | 7 | |a Funktionenraum |0 (DE-588)4134834-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Differentialgleichung |0 (DE-588)4206889-7 |D s |
| 689 | 0 | 1 | |a Funktionenraum |0 (DE-588)4134834-5 |D s |
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| 700 | 1 | |a Schäffer, Juan J. |e Verfasser |4 aut | |
| 830 | 0 | |a Pure and applied mathematics |v 21 |w (DE-604)BV010177228 |9 21 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-001647193 | ||
Datensatz im Suchindex
| _version_ | 1804116957551656960 |
|---|---|
| adam_text | Contents
Preface vj;
PART I
Chapter 1. Geometry of Banach spaces
10. Introduction 3
Summary of the chapter Terminology and notation Continuous
selections
11. Angles, splittings, and dihedra 7
Angular distance and related concepts Splittings Dihedra
12. Coupled spaces 13
Coupled spaces Subspaces Selections and splittings Reflexive spaces
13. The class of subspaces of a Banach space 18
Two metrics The complemented subspaces The class of closed dihedra
A lemma on continuously varying subspaces
14. Hilbert space 26
Notation Angles, splittings, and dihedra The set of subspaces
15. Notes to Chapter 1 31
Chapter 2. Function spaces
20. Introduction 33
Summary of the chapter Further terminology and notation for abstract
spaces. The relations stronger than and Functions and function
spaces The Lebesgue spaces L (X) The space L(A ) / = R and
J = R+ . Translation operators
21. .yf-spaces 41
The lattice -Af(X) Banach spaces in -^ (X) Local closure Completion
The relation =
xv
xvi Contents
22. ^ -spaces 46
The lattices and h.W. Local closure The operators k0 , k, f. Lean
and full spaces The class S- k Associate spaces Thin spaces The
domains R, R_ , R+ . Cutting and splicing at 0 The class (X)
23. ^-spaces 57
The classes -T, F^ The operator T~ The class 3~k Associate spaces
in P The functions a(F; /), j3(F; 1); the spaces L1, L=°, L™ Thin spaces
Thick spaces Cutting and splicing at 0 The classes -T(X), -T^(X)
24. Spaces of continuous functions 76
J^-spaces The class ^^(X) ^ if -spaces on / = R+ and -^Sf-spaces
on J = R
25. Notes to Chapter 2 83
Chapter 3. Linear differential equations
30. Introduction 84
Summary of the chapter Primitives
31. Solutions 86
Existence, uniqueness, and formulas for the solutions Bounds for the
solutions The closedness theorem
32. Associate equations in coupled spaces 89
Associate operator-valued functions Associate equations Green s
Formula
33. D-solutions of homogeneous equations 92
D-solutions and their initial values Examples and comments A result
on associate equations
34. Notes to Chapter 3 97
PART II
Chapter 4. Dichotomies
40. Introduction 101
41. Ordinary dichotomies 102
Definition Dichotomies and solutions in -^ -spaces Examples
Contents xvii
42. Exponential dichotomies 110
Definition Exponential dichotomies and solutions in ^ -spaces Example
43. Dichotomies for associate equations 117
Dichotomies for associate equations Ordinary dichotomies and the
manifolds Xo , X*
44. Finite-dimensional space 120
45. Notes to Chapter 4 122
Chapter 5. Admissibility and related concepts
50. Introduction 124
Summary of the chapter Pairs of Banach function spaces
51. Admissibility 126
Definition and boundedness theorem Regular admissibility Admis¬
sibility and local closure Some remarks on the admissibility of ^ -pairs
and related pairs on i?f Sets of admissible pairs Inadmissible pairs
Equations with scalar A on i?+
52. (B, D)-manifolds 138
Summary of the chapter (concluded) (B, D)-manifolds (B, D)-mani-
folds and admissibility (B, D)-subspaces -^ -pairs and related pairs
Sets of pairs
53. (B, D)-manifolds, admissibility, and the associate equations 149
The polar manifold of a (B, D)-manifold A result on admissible ^ -pairs
54. (B, D)-subspaces and the associate equations 155
The polar manifold of a (B, D)-subspace Implications of admissibility
for the adjoint equation Sets of (B, D)-manifolds and -subspaces for
^ -pairs and related pairs
55. Finite-dimensional space 160
56. Notes to Chapter 5 162
Historical notes Complemented (B, L^-subspaces
Chapter 6. Admissibility and dichotomies
60. Introduction 165
61. The fundamental inequalities 167
xviii Contents
62. Predichotomy behavior of the solutions of the
homogeneous equation 170
Means and slices of solutions Pointwise nonuniform properties of
solutions Miscellaneous corollaries
63. Admissibility, (B, D)-subspaces, and dichotomies:
the general case 179
Ordinary dichotomies Exponential dichotomies Sets of pairs
64. Admissibility, (B, D)-subspaces, and dichotomies:
the equation with A e M(X) 188
The main theorems Sets of pairs
65. Examples and comments 192
Examples with constant A Counterexamples for the direct theorems
Counterexamples for the converse theorems Examples in infinite-
dimensional space Estimation of dichotomy parameters
66. Behavior of the solutions of the associate homogeneous equation 211
Implications of the existence of a (B, D)-subspace Implications of the
existence of a mere (B, D)-manifold A question about dichotomies
67. Notes to Chapter 6 221
Chapter 7. Dependence on A
70. Introduction 223
71. Admissibility classes and (B, D)-subspaces 224
Admissibility classes (B, D)-subspaces
72. Dichotomy classes 237
Exponential dichotomies Ordinary dichotomies
73. Connection in dichotomy classes: Banach spaces 245
Deformation families Connection by arcs in dichotomy classes
74. Connection in dichotomy classes: Hilbert space 251
A bit of motivation Two geometrical lemmas Deformation families
Exponential dichotomies: the general case Exponential dichotomies:
the exceptional case Ordinary dichotomies Finite-dimensional space
75. Notes to Chapter 7 269
Contents xix
Chapter 8. Equations on R
80. Introduction 271
81. (B, D)-dihedra and admissibility 273
The fundamental theorems Some further results
82. Double dichotomies. Connections with admissibility and
(B, D)-dihedra 279
Double dichotomies Examples Connections with admissibility and
(B, D)-dihedra Predichotomy behavior of the solutions of the homo¬
geneous equation
83. Associate equations 293
84. Dependence on A 296
Admissibility classes and closed (B, D)-dihedra Double dichotomy
classes Connection in double-dichotomy classes
PART III
Chapter 9. Ljapunov s method
90. Introduction 311
Summary of the chapter Pointwise properties of the solutions. Excep¬
tional sets
91. Ljapunov functions 316
Ljapunov functions Total derivatives
92. Exponential dichotomies 320
93. Ordinary dichotomies 327
94. Notes to Chapter 9 332
Chapter 10. Equations with almost periodic A
100. Introduction 333
Summary of the chapter Spaces of almost periodic functions Almost
periodic equations and solutions. Preliminary facts
101. The condition X0 tca = {0} 338
102. Exponential dichotomies 341
xx Contents
103. Reflexive and finite-dimensional spaces 343
104. Notes to Chapter 10 345
Equations on R+ The theory of Favard
Chapter 11. Equations with periodic A
110. Introduction 348
Summary of the chapter Spaces of periodic functions Properties of U
111. Floquet representation 351
112. Periodic equations and periodic solutions 354
113. The solutions of the homogeneous equation 358
D-solutions Double dichotomies Examples Exponential and double
exponential dichotomies
114. Individual periodic equations 369
Chapter 12. Higher-order equations
120. Introduction 373
Summary of the chapter nth primitive functions
121. The (m - - l)st-order equation 376
122. Admissibility and (B, D)-manifolds 381
123. The main theorems 386
References 393
Index Author and subject 399
Notation 402
|
| any_adam_object | 1 |
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| building | Verbundindex |
| bvnumber | BV002558372 |
| classification_rvk | SK 520 SK 600 |
| ctrlnum | (OCoLC)257860567 (DE-599)BVBBV002558372 |
| discipline | Mathematik |
| edition | 2. print. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:46:46Z |
| institution | BVB |
| language | English |
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| oclc_num | 257860567 |
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| physical | XX, 404 S. |
| publishDate | 1967 |
| publishDateSearch | 1967 |
| publishDateSort | 1967 |
| publisher | Acad. Pr. |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Massera, José L. Verfasser aut Linear differential equations and function spaces José Luis Massera ; Juan Jorge Schäffer 2. print. New York u.a. Acad. Pr. 1967 XX, 404 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 21 Lineare Differentialgleichung (DE-588)4206889-7 gnd rswk-swf Funktionenraum (DE-588)4134834-5 gnd rswk-swf Lineare Differentialgleichung (DE-588)4206889-7 s Funktionenraum (DE-588)4134834-5 s DE-604 Schäffer, Juan J. Verfasser aut Pure and applied mathematics 21 (DE-604)BV010177228 21 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001647193&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Massera, José L. Schäffer, Juan J. Linear differential equations and function spaces Pure and applied mathematics Lineare Differentialgleichung (DE-588)4206889-7 gnd Funktionenraum (DE-588)4134834-5 gnd |
| subject_GND | (DE-588)4206889-7 (DE-588)4134834-5 |
| title | Linear differential equations and function spaces |
| title_auth | Linear differential equations and function spaces |
| title_exact_search | Linear differential equations and function spaces |
| title_full | Linear differential equations and function spaces José Luis Massera ; Juan Jorge Schäffer |
| title_fullStr | Linear differential equations and function spaces José Luis Massera ; Juan Jorge Schäffer |
| title_full_unstemmed | Linear differential equations and function spaces José Luis Massera ; Juan Jorge Schäffer |
| title_short | Linear differential equations and function spaces |
| title_sort | linear differential equations and function spaces |
| topic | Lineare Differentialgleichung (DE-588)4206889-7 gnd Funktionenraum (DE-588)4134834-5 gnd |
| topic_facet | Lineare Differentialgleichung Funktionenraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001647193&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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