D`Alembert-Liouville-Ostrogradskii formula and related results

Анотація

Results, that generalize previous important results of the d'`Alembert- Liouville-Ostrogradskii formula type by F.S. Rofe-Beketov, are obtained. The 2p × 2p fundamental solution of the first order system is recovered by its 2p×p block Y₀. 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×p blocks of Y₀ on the interval is not required.