Об одном операторе интегрирования

Abstract

In this paper we study an operator, which is a linear combination of the model operator of integration and its adjoint. We prove that the operator is bounded and construct its adjoint. For the considered operator, which is not self-adjoint, a local node is determined and the node characteristic function is calculated. A semigroup generated by the operator is defined, which leads to a Cauchy problem for a second order differential equation. We note that the operator considered is not always dissipative and the operator node characteristic function possesses several features studied in the paper. The directions of further investigation are proposed.