The article provides a systematic presentation of an operator pattern that forms the basis of a certain approach to inverse problems in mathematical physics – the boundary control method. The pattern is based on the triangular factorization of operators. Not only solves it inverse problems but also provides functional models for an important class of symmetric semibounded operators. These models are constructed by using an evolutionary dynamical system determined by the operator.
Belishev et al. (Wed,) studied this question.