Zero localization and asymptotic behavior of orthogonal polynomials of jacobi-sobolev

Abstract

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 [-√(1+2C, √ 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 ortogonal polynomials under certain restrictions.