On Linear Relations Generated by a DiRerential Expression and by a Nevanlinna Operator Function

Abstract

The families of maximal and minimal relations generated by a differential expression with bounded operator coe±cients and by a Nevanlinna operator function are defined. These families are proved to be holomorphic. In the case of finite interval, the space of boundary values is constructed. In terms of boundary conditions, a criterion for the restrictions of maximal relations to be continuously invertible and a criterion for the families of these restrictions to be holomorphic are given. The operators inverse to these restrictions are stated to be integral operators. By using the results obtained, the existence of the characteristic operator on the finite interval and the axis is proved.