# zbMATH — the first resource for mathematics

Comments on almost automorphic and almost periodic functions in Banach spaces. (English) Zbl 1096.34036
The paper provides an introductory discussion of almost-periodic and (uniformly continuous) Bochner almost automorphic functions, a formulation (without proofs) of two theorems about the existence of solutions of $$x'=Ax+f$$ on $$\mathbb{R}$$ which are almost automorphic resp. almost-periodic, with $$A$$ an infinitesimal generator of an exponentially stable $$C_0$$-semigroup and $$f:\mathbb{R}\to X$$ almost automorphic resp. Stepanoff $$S^2$$-almost-periodic, $$X$$ reflexive resp. Hilbert space. (For theorem 2.6 the proof of (2.9) is not correct.)

##### MSC:
 34G10 Linear differential equations in abstract spaces 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions 47D06 One-parameter semigroups and linear evolution equations 35B15 Almost and pseudo-almost periodic solutions to PDEs
##### Keywords:
evolution equation; almost-periodic; $$C_0$$-semigroup