Corduneanu Almost Periodic Oscillations and Waves

1. Auflage 2009
ISBN: 978-0-387-09819-7
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 308 Seiten

Autoren/Hrsg.

Corduneanu, Constantin

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;1 Introduction;9
4;2 Metric Spaces and Related Topics;22
4.1;2.1 Metric Spaces;22
4.2;2.2 Banach Spaces and Hilbert Spaces;27
4.3;2.3 Function Spaces: Continuous Case;35
4.4;2.4 Completion of Metric Spaces;40
4.5;2.5 Function Spaces: Measurable Case;45
5;3 Basic Properties of Almost Periodic Functions;56
5.1;3.1 The Space AP1(R, C);56
5.2;3.2 The Space AP(R, C);60
5.3;3.3 The Space S(R, C);67
5.4;3.4 Besicovitch Spaces; the Mean Value;71
5.5;3.5 The Space AP(R, X), X-Banach Space;78
5.6;3.6 Almost Periodic Functions Depending on Parameters;88
5.7;3.7 Variations on the Theme of Almost Periodicity;94
6;4 Fourier Analysis of Almost Periodic Functions;103
6.1;4.1 General Remarks;103
6.2;4.2 The Fourier Series Associated to an Almost Periodic Function;105
6.3;4.3 Convergence of Fourier Series;111
6.4;4.4 Summability of Fourier Series;117
6.5;4.5 The Fourier Series of Almost Periodic Functions in Banach Spaces;123
6.6;4.6 Further Topics Related to Fourier Series;132
7;5 Linear Oscillations;137
7.1;5.1 The Equation x.(t) = f(t);137
7.2;5.2 Weakly Almost Periodic Functions;143
7.3;5.3 The Equation x.(t) = f(t) in Banach Spaces;150
7.4;5.4 Linear Oscillations Described by Ordinary Differential Equations;156
7.5;5.5 Linear Periodic and Almost Periodic Oscillations in Systems Described by Convolution Equations;162
7.6;5.6 Further Results on Almost Periodic Oscillations in Linear Time-Invariant Systems;171
7.7;5.7 Almost Periodic Oscillations in Linear Time-Varying Systems;184
8;6 Almost Periodic Nonlinear Oscillations;191
8.1;6.1 Quasilinear Systems;191
8.2;6.2 Separated Solutions: Amerio’s Theory;196
8.3;6.3 The Second-Order Equation of Nonlinear Oscillations (Li´enard’s Type);202
8.4;6.4 Equations with Monotone Operators;207
8.5;6.5 Gradient Type Systems;214
8.6;6.6 Qualitative Differential Inequalities;224
8.7;6.7 Further Results on Nonlinear Almost Periodic Oscillations; Perturbed Systems;231
8.8;6.8 Oscillations in Discrete Processes;236
8.9;6.9 Oscillations in Systems Governed by Integral Equations;245
9;7 Almost Periodic Waves;253
9.1;7.1 Some General Remarks;253
9.2;7.2 Periodic Solitary Waves in One-Dimensional Hyperbolic and Parabolic Structures;257
9.3;7.3 Almost Periodic Heat Waves;262
9.4;7.4 Almost Periodic Waves; a Linear Case;273
9.5;7.5 Almost Periodic Waves; a Mildly Nonlinear System;280
9.6;7.6 A Case with Data on Characteristics;286
9.7;7.7 Miscellanea;292
9.8;7.8 Quasi-periodic Waves;300
10;References;307
11;Index;312