On the determination of self-adjoint differential operators on the semiaxis
The author studies the inverse problem of recording the differential operators \((\ell, U_\xi)\) in the equations \[ ly = y^{(n)} + \sum^{n - 2}_{\nu = 0} p_\nu (x)y^{(\nu)} = \lambda y, \quad x > 0,\;p_\nu(x) \in {\mathcal L} (0, \infty), \] \[ U_\xi (y) = y^{(\sigma_\xi)} (0) + \sum^{\sigma_\xi - 1}_{\nu = 0} u_{\xi \nu} y^{(\nu)} (0), \quad \xi = 1, \dots, n,\;0 \leq \sigma_\xi \leq n - 1 \] from the Weil solutions \(\Phi_1 (x, \lambda), \dots, \Phi_n (x, \lambda)\) and the corresponding Weil matrix \({\mathfrak M} (\lambda)\) with entries \(U_{km} (\lambda) = U_m (\Phi_k)\). The techniques use previous results of the author published in [Mat. Sb. 182, No. 3, 431-456 (1991; Zbl 0782.34021)].
scientific article; zbMATH DE number 846505
scientific article