The Krein string and characteristic functions of non-self-adjoint operators

The operator generated by the Krein string is investigated in the framework of the extension theory of symmetric operators. A simple proof of the complete non-self-adjointness of the operator is proposed. The scattering function of the string is obtained with the help of the Derkach-Malamud formula for characteristic functions of almost solvable extensions. Bibliography: 16 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 327, 2005, pp. 115–134.