International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 9, Pages 521-534

On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces

Samuel Zaidman

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.


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(), X is almost-periodic, while A is a linear operator, 𝒟(A)XX. If the solution u() is likewise almost-periodic, X, we establish connections between their Bohr-transforms, uˆ(λ) and fˆ(λ).