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An estimate of Green's function of the bounded solutions problem for theordinary differential equation $x'(t)-Bx(t)=f(t)$ is proposed. It is assumedthat the matrix coefficient $B$ is triangular. This estimate is ageneralization of the estimate of the matrix exponential proved by Ch. F. VanLoan.

An estimate of Green's function of the problem of bounded solutions in the case of a triangular coefficient