Almost Periodic Oscillations and Waves (eBook)

Constantin Corduneanu (Autor)

eBook Download: PDF

2009 | 2009
VIII, 308 Seiten
Springer New York (Verlag)
978-0-387-09819-7 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 29.4.2009
• Zusatzinfo: VIII, 308 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Calculus • Continuum Mechanics • fourier analysis • Linear Oscillations • Mechanics • Metric Spaces • nonlinear oscillations • Partial differential equations • vibrations
• ISBN-10: 0-387-09819-4 / 0387098194
• ISBN-13: 978-0-387-09819-7 / 9780387098197