Method of Mathematical Theory of Moments

Infinite matrices play an important role in many aspects of analysis, algebra, differential equations, and the theory of mechanical vibrations. Jacobi matrices are interesting because they are the simplest representatives of symmetric operators in infinite-dimensional space. they are used in interpolation theory, quantum physics, moment problem. In this paper, based on the elements of Jacobi matrix, it will be determined the type of the operator that occurs when processing the results of measurements of random variables. The first type of operators are matrices, for which the moment problem has a unique solution, and Jacobi matrix generates a specific moment problem. The second type of operators are matrices, for which the moment problem has many solutions, and Jacobi matrix is said to generate an indeterminate moment problem.