Decomposition of Phase Space for Linear Volterra Difference Equations in a Banach Space

抄録

We study the spectrum of the solution operator for a linear Volterra difference equation in a Banach space, and obtain the decomposition of the phase space, together with that of the variation of constants formula in the phase space. As an application, we establish the existence of almost periodic solutions for forced linear Volterra difference equations with an almost periodic forcing term.