Author(s): Constantin Corduneanu
Edition: 1
Publisher: Springer
Year: 2008
Language: English
Pages: 313
0387098186......Page 1
Contents......Page 7
Preface......Page 5
1. Introduction......Page 9
2.1 Metric Spaces......Page 22
2.2 Banach Spaces and Hilbert Spaces......Page 27
2.3 Function Spaces: Continuous Case......Page 35
2.4 Completion of Metric Spaces......Page 40
2.5 Function Spaces: Measurable Case......Page 45
3.1 The Space AP[sub(1)](R, C)......Page 56
3.2 The Space AP(R, C)......Page 60
3.3 The Space S(R, C)......Page 67
3.4 Besicovitch Spaces; the Mean Value......Page 71
3.5 The Space AP(R,X), X-Banach Space......Page 78
3.6 Almost Periodic Functions Depending on Parameters......Page 88
3.7 Variations on the Theme of Almost Periodicity......Page 94
4.1 General Remarks......Page 103
4.2 The Fourier Series Associated to an Almost Periodic Function......Page 105
4.3 Convergence of Fourier Series......Page 111
4.4 Summability of Fourier Series......Page 117
4.5 Fourier Series of Almost Periodic Functions in Banach Spaces......Page 123
4.6 Further Topics Related to Fourier Series......Page 132
5.1 The Equation ẋ(t) = f(t)......Page 137
5.2 Weakly Almost Periodic Functions......Page 143
5.3 The Equation ẋ = f(t) in Banach Spaces......Page 150
5.4 Linear Oscillations Described by Ordinary Differential Equations......Page 156
5.5 Linear Periodic and Almost Periodic Oscillations in Systems Described by Convolution Equations......Page 162
5.6 Further Results on Almost Periodic Oscillations in Linear Time–Invariant Systems......Page 171
5.7 Almost Periodic Oscillations in Linear Time-Varying Systems......Page 184
6.1 Quasilinear Systems......Page 191
6.2 Separated Solutions: Amerio's Theory......Page 196
6.3 The Second-Order Equation of Nonlinear Oscillations (Liénard's Type)......Page 202
6.4 Equations with Monotone Operators......Page 207
6.5 Gradient Type Systems......Page 214
6.6 Qualitative Differential Inequalities......Page 224
6.7 Further Results on Nonlinear Almost Periodic Oscillations; Perturbed Systems......Page 231
6.8 Oscillations in Discrete Processes......Page 236
6.9 Oscillations in Systems Governed by Integral Equations......Page 245
7.1 Some General Remarks......Page 253
7.2 Periodic Solitary Waves in One-Dimensional Hyperbolic and Parabolic Structures......Page 257
7.3 Almost Periodic Heat Waves......Page 262
7.4 Almost Periodic Waves; a Linear Case......Page 273
7.5 Almost Periodic Waves; a Mildly Nonlinear System......Page 280
7.6 A Case with Data on Characteristics......Page 286
7.7 Miscellanea......Page 292
7.8 Quasi-periodic Waves......Page 300
References......Page 307
O......Page 312
W......Page 313
