Zero location and asymptotic behavior of orthogonal polynomials of Jacobi-Sobolev

Abstract

[EN] In this article we consider the Sobolev orthogonal polynomials associated to the Jacobi's measure on [-1,1] . It is proven that for the class of monic Jacobi-Sobolev orthogonal polynomials, the smallest closed interval that contains its real zeros is $[-\sqrt{1 + 2C}, \sqrt{1 + 2C}]$ with C a constant explicitly determined. The asymptotic distribution of those zeros is studied and also we analyze the asymptotic comparative behavior between the sequence of monic Jacobi-Sobolev orthogonal polynomials and the sequence of monic Jacobi orthogonal polynomials under certain restrictions.

[ES] Para la clase de los polinomios ortogonales mónicos de Jacobi-Sobolev probamos que el menor intervalo cerrado que contiene a sus ceros reales es $[-\sqrt{1 + 2C}, \sqrt{1 + 2C}]$, donde C es una constante explícitamente determinada. Estudiamos la distribución asintótica de tales ceros, así como también analizamos el comportamiento asintótico de los polinomios ortogonales mónicos de Jacobi-Sobolev respecto a los polinomios ortogonales mónicos de Jacobi, bajo ciertas restricciones.