On the Spectrum of almost periodic solutions of an abstract differential equation

Abstract

If a linear operator A in a Banach space satisfies certain conditions, then the spectrum of any almost periodic solution of the differential equation u′ = Au + f is shown to be identical with the spectrum of f, where f is a Stepanov almost periodic function.

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

“…(ii) In [6] the equation is (1.1) and f is continuous almost-periodic in Stepanoff S P -sense; the operator A is closed in X. One gets the equality…”