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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
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