D'Alembert–Liouville–Ostrogradskii formula and related results

Results, that generalize previous important results of the d'Alembert–Liouville–Ostrogradskii formula type by F. S. Rofe-Beketov, are obtained. The $2p\times 2p$ fundamental solution of the first order system is recovered by its $2p\times p$ block $Y_0$. Applications to the asymptotics of the continuous analogs of polynomial kernels and to the pseudo-Hermitian quantum mechanics are treated. Similar to the F. S. Rofe-Beketov results the invertibility of the $p \times p$ blocks of $Y_0$ on the interval is not required.