Resumen de Quasi orthogonal Jacobi polynomials and best one-sided image approximation to step functions

Jorge Bustamante González, Reinaldo Martínez Cruz, José María Quesada Teruel

• We find the polynomials of the best one-sided approximation to a step function on [−1,1]. We prove that these polynomials are obtained by Hermite interpolation at the zeros of some quasi orthogonal Jacobi polynomials. We discuss the cases when there is uniqueness and, if there is not, we determine the extremal points of the convex set of the best approximants.