Linear Relations Generated by Integral Equations with Nevanlinna Operator Measures

Abstract

We  consider a family of minimal relations \(\mathcal{L}_{0}(\lambda)\) generated by an integral equation with a Nevanlinna operator measure and give a description the families \(\mathcal{L}_{0}(\lambda)\), \(\mathcal{L}^{*}_{0}(\overline{\lambda})\) , where \(\lambda\in\mathbb{C}\). We prove that the  families \(\mathcal{L}_{0}(\lambda)\), \(\mathcal{L}^{*}_{0}(\overline{\lambda})\) are holomorphic   and give a description of  families relations \(T(\lambda)\) such that  \(\mathcal{L}_{0}(\lambda)\subset T(\lambda)\subset\mathcal{L}^{*}_{0}(\overline{\lambda})\) and \(T^{-1}(\lambda)\) are bounded everywhere defined operators. The results obtained are applied to the proof of the existence of a characteristic operator for the integral equation.