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Almost Periodic Oscillations and Waves / by Constantin Corduneanu
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: New York, NY : Springer-Verlag New York, 2009Description: Online-Ressource (digital)ISBN:- 9780387098197
- 515.39 23
- 515.48 23
- 515.2433
- QA404
Contents:
Summary: Metric Spaces and Related Topics -- Basic Properties of Almost Periodic Functions -- Fourier Analysis of Almost Periodic Functions -- Linear Oscillations -- Almost Periodic Nonlinear Oscillations -- Almost Periodic Waves.Summary: 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. The first half of the book lays the groundwork, noting the basic properties of almost periodic functions, while the second half of this work addresses applications whose main emphasis is on the solvability of ordinary or partial differential equations in the class of almost periodic functions. Key topics include: An introduction to metric spaces; Definition of several classes of almost periodic functions, including those of Bohr, Besicovitch, and Stepanov; Classical results on the mean value property; Convergence of Fourier series to any almost periodic function; Almost periodic solutions for ODEs in a linear setting; Almost periodic nonlinear oscillations; Almost periodic waves, including heat waves. The reader is taken from elementary and well-known facts through the latest results in almost periodic oscillation and waves. This is the first text to present these latest results. 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.PPN: PPN: 1647883504Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
CONTENTS; Preface; 1 Introduction; 2 Metric Spaces and Related Topics; 2.1 Metric Spaces; 2.2 Banach Spaces and Hilbert Spaces; 2.3 Function Spaces: Continuous Case; 2.4 Completion of Metric Spaces; 2.5 Function Spaces: Measurable Case; 3 Basic Properties of Almost Periodic Functions; 3.1 The Space AP 1 (R, C); 3.2 The Space AP(R, C); 3.3 The Space S(R, C); 3.4 Besicovitch Spaces; the Mean Value; 3.5 The Space AP(R, X), X-Banach Space; 3.6 Almost Periodic Functions Depending on Parameters; 3.7 Variations on the Theme of Almost Periodicity; 4 Fourier Analysis of Almost Periodic Functions
4.1 General Remarks4.2 The Fourier Series Associated to an Almost Periodic Function; 4.3 Convergence of Fourier Series; 4.4 Summability of Fourier Series; 4.5 Fourier Series of Almost Periodic Functions in Banach Spaces; 4.6 Further Topics Related to Fourier Series; 5 Linear Oscillations; 5.1 The Equation ?(t) =f(t); 5.2 Weakly Almost Periodic Functions; 5.3 The Equation ?(t) = f(t)in Banach Spaces; 5.4 Linear Oscillations Described by Ordinary DifferentialEquations; 5.5 Linear Periodic and Almost Periodic Oscillations in SystemsDescribed by Convolution Equations
5.6 Further Results on Almost Periodic Oscillations in LinearTime-Invariant Systems5.7 Almost Periodic Oscillations in Linear Time-Varying Systems; 6 Almost Periodic Nonlinear Oscillations; 6.1 Quasilinear Systems; 6.2 Separated Solutions: Amerio's Theory; 6.3 The Second-Order Equation of Nonlinear Oscillations (Liénard's Type); 6.4 Equations with Monotone Operators; 6.5 Gradient Type Systems; 6.6 Qualitative Differential Inequalities; 6.7 Further Results on Nonlinear Almost Periodic Oscillations; Perturbed Systems; 6.8 Oscillations in Discrete Processes
6.9 Oscillations in Systems Governed by Integral Equations7 Almost Periodic Waves; 7.1 Some General Remarks; 7.2 Periodic Solitary Waves in One-Dimensional Hyperbolicand Parabolic Structures; 7.3 Almost Periodic Heat Waves; 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; 7.7 Miscellanea; 7.8 Quasi-periodic Waves; References; Index
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