Zeros of Sobolev orthogonal polynomials following from coherent pairs
The location of the zeros of polynomials orthogonal with respect to an inner product involving derivatives (a Sobolev inner product) is not a simple question. Nevertheless, if the two measures involved in the inner product form a coherent pair, all the zeros of the Sobolev orthogonal polynomials are real and simple. In this paper the authors study their relative location, namely when they interlace with the zeros of standard orthogonal polynomials (Laguerre or Jacobi) or separate those of Sobolev orthogonal polynomials of lower degree. As in the classical case, Gauss quadrature proves to be a useful tool.
scientific article; zbMATH DE number 1743073