On characteristic functions of generalized resolvents generated by integral equations with operator measures

Abstract

We consider a symmetric minimal relation L0 generated by an integral equation with operators measures. We describe the generalized resolvents of L0 using the characteristic function M(?) (? ? C), i.e., a function that has the property (Im?)?1ImM(?) ? 0. We obtain a necessary and sufficient condition for a holomorphic function M(?) to be a characteristic function of a generalized resolvent. We give a detailed example of finding the characteristic function.