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Almost Periodic Oscillations and Waves

  • Book
  • © 2009

Overview

  • Author is a renowned expert in the fields of PDEs and ODEs
  • An introduction to metric spaces
  • Presentation of several classes of almost periodic functions, including those of Bohr, Besicovitch, and Stepanov
  • Convergence of Fourier Analysis to almost any periodic function
  • Almost periodic solutions for ODEs in a linear setting
  • Almost periodic nonlinear oscillations
  • Almost periodic waves, including heat waves

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Table of contents (7 chapters)

Keywords

About this book

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.

Reviews

From the reviews:

"In writing this book the author aims to make the concept of almost periodicity more accessible to the broader audience of mathematicians, scientists, and engineers who are interested in the theory of oscillations and waves. The book is divided into two parts. … The book is well organized." (Vladimir Sh. Burd, Mathematical Reviews, Issue 2009 i)

Authors and Affiliations

  • Dept. Mathematics, University of Texas, Arlington, Arlington, U.S.A.

    Constantin Corduneanu

About the author

 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.

Bibliographic Information

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