On Characteristic Functions of Generalized Resolvents Generated by Integral Equations with Operator Measures

Abstract

We consider a symmetric
minimal relation \(L_{0}\) generated by an integral equation with ope\-ra\-tors measures.
We describe the generalized resolvents of \(L_{0}\) using the characteristic function \(M(\lambda)\) \((\lambda\in\mathbb{C})\), i.e., a function that has the property \((\mathrm{Im}\lambda)^{-1}\mathrm{Im}M(\lambda)\geqslant0\).
We obtain a necessary and sufficient condition for a holomorphic function \(M(\lambda)\) to be a characteristic function of a generalized resolvent.
We give a detailed example of finding the characteristic function.