Invertible linear relations generated by an integral equation with Nevanlinna measure
The families of maximal and minimal relations generated by integral equations with Nevanlinna operator measure and non-selfadjoint operator measure are defined. The author proves that if a restriction of a maximal relation is continuously invertible, then the inverse operator is integral. The special case is considered when the convergence of non-selfadjoint operator measures implies the convergence of the corresponding integral operators inverse to restrictions of maximal relations. A theorem which establishes a sufficient condition for the validity of such implication is proved. As an application, the author considers the differential equations with singular potentials described by \textit{A. M. Savchuk} and \textit{A. A. Shkalikov} [Math. Notes 66, No. 6, 741--753 (1999); translation from Mat. Zametki 66, No. 6, 897--912 (1999; Zbl 0968.34072)].
scientific article; zbMATH DE number 6152675