Corduneanu Almost Periodic Oscillations and Waves

2009
ISBN: 978-0-387-09819-7
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 308 Seiten

This text is well-designed with respect to the exposition from the preliminary to the more advanced and the applications interwoven throughout. It provides the essential foundations for the theory as well as the basic facts relating to almost periodicity.  In six structured and self-contained chapters, the author unifies the treatment of various classes of almost periodic functions, while uniquely addressing oscillations and waves in the almost periodic case. This is the first text to present the latest results in almost periodic oscillations and waves. The presentation level and inclusion of several clearly presented proofs make this work ideal for graduate students in engineering and science. The concept of almost periodicity is widely applicable to continuuum mechanics, electromagnetic theory, plasma physics, dynamical systems, and astronomy, which makes the book a useful tool for mathematicians and physicists.

 C. Corduneanu has published extensively: Integral Equations and Applications, HC, 1991, Cambridge Univ. Press, 978-0521340502, 376 pp. Functional Equations with Causal Operators (Stability and Control: Theory, Methods and Applications, 16)  (Kindle Edition), $119.95, Taylor & Francis, 2007 Functional Equations with Causal Operators (Stability and Control: Theory, Methods and Applications, 16)  (HC Edition), $119.95, CRC, 2002, 978-0415271868 with I. Sandberg, Volterra Equations and Applications (Stability and Control), $179.00, 512pp, CRC, 2000, 978-9056991715 The author is a renowned expert in the fields of ordinary and partial differential equations.

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