Sobre polinomios ortogonales con producto interno de sóbolev

Abstract

Orthogonal Polynomials is an important branch of Mathematics. They appear for the first time at the end of the 18th century. These polynomials became the center of multiple studies in differents areas such as quantum mechanics, theory of Hilbert spaces and Statistics. In this paper we study the article "Orthogonal polynomials in Sobolev spaces: old and new directions" by F. Marcellan, M. Alfaro and M.L. Rezola. We carry out a theoretical synthesis that argues the theory discussed in this article, and we interpret and extend the demonstrations of approximation of functions in a Sobolev spaces by orthogonal polynomials in the sense of least squares.