MR2271235 Nagabuchi, Yutaka Yutaka NAGABUCHI Decomposition of Phase Space for Linear Volterra Difference Equations in a Banach Space Funkcialaj Ekvacioj. Serio Internacia 49 2006 269--290 http://fe.math.kobe-u.ac.jp/FE/FullPapers/49-2/49_269.pdf http://www.ams.org/mathscinet-getitem?mr=MR2271235 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. Volterra difference equation, Decomposition of phase space, Variation of constants formula in the phase space, Almost periodic solution, Bohr spectrum. 39A11, 34K14. 49-269 2006 Decomposition of Phase Space for Linear Volterra Difference Equations in a Banach Space NAGABUCHI, Yutaka Yutaka NAGABUCHI 1 Edmunds, D. E.; Evans, W. D. Spectral Theory and Differential Operators Oxford Science Publications, Clarendon Press, Oxford 1987 MR0929030 2 Elaydi, S. An Introduction to Difference Equations Springer, Berlin, New-York 1996 MR1410259
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