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On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces. (English) Zbl 1001.34039

The author considers the abstract differential equations \(u' (t) = A u(t) + f(t)\) and \(u''(t) = A u(t) + f(t)\) for \(t \in \mathbb{R}\) and the linear operator \(A\) in a Banach space \(X\). He studies properties of the solution \(u(\cdot)\) in case that \(f(\cdot)\) is almost-periodic.

MSC:

34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
34G10 Linear differential equations in abstract spaces
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