International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 9, Pages 521-534
doi:10.1155/S0161171201012352
On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces
Départment de Mathématique et de Statistique, Université de Montréal, Montréal H3C 3J7, QC, Canada
Received 11 March 2001; Revised 4 July 2001
Copyright © 2001 Samuel Zaidman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We consider abstract differential equations of the form u′(t)=Au(t)+f(t) or u″(t)=Au(t)+f(t) in Banach spaces X, where f(⋅), ℝ→X is almost-periodic, while A is a linear operator, 𝒟(A)⊂X→X. If the solution u(⋅) is likewise almost-periodic, ℝ→X, we establish connections between their Bohr-transforms, uˆ(λ) and fˆ(λ).