Method of Mathematical Theory of Moments

Abstract

Infinite matrices play an important role in many aspects of analysis, algebra, differential equations, andthetheory of mechanical vibrations.Jacobi matrices are interestingbecause 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, basedon the elements of Jacobi matrix, itwill be determinedthe type of the operator that occurs when processing the results of measurements of random variables. The first type of operators arematrices,for which the moment problem has a unique solution, and Jacobi matrix generates a specific moment problem. The second type of operators arematrices, for which the moment problem has many solutions, and Jacobi matrix is said to generate an indeterminate moment problem.