The connection between the Sturm-Liouville systems and the triangular model of coupling of dissipative and antidissipative operators (Q2822185)

In the paper under review, a Sturm-Liouville system is considered. The author obtains a useful representation of the solutions of this system which is connected with the resolvents of the operators from the large class of nonselfadjoint nondissipative operators. In the paper, the case of a nonselfadjoint operator with finite dimensional imaginary part in a Hilbert space is studied. The property of the solution of the Sturm-Liouville system is obtained when the Volterra operator \( B \) is a coupling of a dissipative operator and an antidissipative one with zero spectra. The obtained results can be applied in problems concerning the connection between the theory of commuting nonselfadjoint operators and soliton theory.