The proposed monograph develops the operator method for problems of analysis, mathematical physics of heterogeneous environments and the theory of dependence recovery. The operator method opens up the possibility of solving a problem for a piecewise homogeneous environment by reducing to the corresponding problem for a homogeneous environment. As a result, the solution is obtained in a 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 by methods of potential theory. The solution obtained with the help of transformation operators is in the form convenient for studying 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 the problems of piecewise homogeneous environments. In turn, with the help of integral transformations, it was possible to effectively build the main transformation operators. The stochastic variant of the problem of restoration of functional dependencies is considered. The device for solving this problem is the method of transformation operators. The problem of finding correct algorithms that recognize this sample without errors is also considered.