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.