Almost Periodic Type Functions and Ergodicity

From the reviews: "In this monograph, the function classes considered are; Bohr almost periodic ... asymptotic ap AAP, Eberlein weakly ap WAP ... and X a Banach space. These are introduced and discussed in some detail; then the author addresses their application to the asymptotic study of solutions of differential equations ... . One should be grateful for the wealth of material presented, collecting, unifying and sometimes generalizing many recent results. Consequently, the book can serve as an introduction ... and it would be especially good for seminars." (Hans F. Gunzler, Zentralblatt MATH, Vol. 1068 (19), 2005)

• 1 Almost periodic type functions.- 1.1.- 1.2 Asymptotically almost periodic functions.- 1.3 Weakly almost periodic functions.- 1.4 Approximate theorem and applications.- 1.5 Pseudo almost periodic functions.- 1.6 Converse problems of Fourier expansions.- 1.7 Almost periodic type sequences.- 2 Almost periodic type differential equations.- 2.1 Linear differential equations.- 2.2 Partial differential equations.- 2.3 Means, introversion and nonlinear equations.- 2.4 Regularity and exponential dichotomy.- 2.5 Equations with piecewise constant argument.- 2.6 Equations with unbounded forcing term.- 2.7 Almost periodic structural stability.- 3 Ergodicity and abstract differential equations.- 3.1 Ergodicity and regularity.- 3.2 Ergodicity and nonlinear equations.- 3.3 Semigroup of operators and applications.- 3.4 Delay differential equations.- 3.5 Spectrum of functions.- 3.6 Abstract Cauchy Problems.- 4 Ergodicity and averaging methods.- 4.1 Ergodicity and its properties.- 4.2 Quantitative theory.- 4.3 Perturbations of noncritical linear systems.- 4.4 Qualitative theory of averaging methods.- 4.5 Averaging methods for functional equations.- Notations.