El problema de los momentos de Hamburger

Abstract

The study of the Hamburger moment problem will be addressed through operator theory in Hilbert spaces. The first three chapters will provide a foundation for this study. Chapter 1 will deal with the problem of self-adjoint extensions of an operator. Chapter 2 will focus on proving the spectral representation theorem for self-adjoint operators. Chapter 3 considers real sequences through algebra to facilitate their later study. Subsequently, chapters 4 and 5 will provide an answer to the problem. Chapter 4 will examine Jacobi operators and orthogonal polynomials, two mathematical entities closely related to the moment problem. Chapter 5 brings together all the material studied to address the existence and determination (uniqueness) of the problem, as well as its relation to Jacobi operators and orthogonal polynomials. Finally, chapter 6 presents the conclusions of the study