Transformation operators for boundary value problems, integral representations, and dependency recovery

The proposed monograph develops the operator method for analyzing problems, mathematical physics of inhomogeneous media and the theory of dependency recovery. The operator method opens up the possibility of solving a problem for a piecewise homogeneous environment to the corresponding task for a homogeneous medium. As a result, the solution is obtained in the form convenient for study. The method of transformation operators allows in some cases to clarify the results obtained by the method of integral transformations or methods of potential theory. The solution obtained using conversion operators has a form convenient to study asymptotic properties. At the same time, the computational algorithm is significantly simplified, the behavior of the solution near the border is determined.
The method of transformation operators reveals the nature of integral transformations adapted to solve problems of piecewise homogeneous media.
In turn, with the help of integral transformations, it was possible to effectively construct the main transformation operators. A stochastic version of the task of restoring functional dependencies is considered. The solution of this task is the method of transformation operators. The problem of finding the correct algorithms that recognize this sample without errors is also considered