Almost automorphic type and almost periodic type functions in abstract spaces. (English) Zbl 1279.43010

Diagana, Toka

Cham: Springer (ISBN 978-3-319-00848-6/hbk; 978-3-319-00849-3/ebook). xiv, 303 p. (2013).

The book under review provides an introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, pseudo-almost automorphy, and some of their recent generalizations.
The author presents various sufficient conditions ensuring existence, uniqueness, boundedness and stability of solutions to different classes of first, second and higher order abstract differential, difference and integro-differential equations with coefficients belonging to the above mentioned spaces of functions. Applications to particular problems arising in control system theory are given as well.
The prerequisites for the book is the basic introductory course in real analysis. Depending on the background of the students, the book may be suitable for beginning graduate and/or advanced undergraduate courses. Additionally, it may be of interest to researchers in mathematics, engineering and physics, and all related areas.

Reviewer: Dian K. Palagachev (Bari)

MSC:

43A60	Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
34-02	Research exposition (monographs, survey articles) pertaining to ordinary differential equations
34K14	Almost and pseudo-almost periodic solutions to functional-differential equations

Keywords:

abstract spaces; almost periodic functions; almost automorphic functions; ordinary differential equations; difference equations