The Gelfand-Shilov type estimate for Green's function of the bounded solutions problem (Q1617240)

The authors obtain an estimate of the Green's function related to the bounded solutions on the real line of the linear vectorial problem \[ x'(t)=A\;x(t)+f(t) \] with \(A\) a given constant matrix with no eigenvalues at the imaginary axis. The proof follows from the Newton's interpoling formulas of the characteristic polynomial of the equation.