Modified (0, 2)-Interpolation on the Roots of Jacobi Polynomials. II (Convergence)

In [4] A. M. Chak, A. Sharma and J. Szabados characterized the Jacobi matrices P(α,β), (α,β > −1) for which the (0,2)-interpolation problem is regular. It follows from their result, that if n is odd and α = β, or if α, β are both odd integers and n > 1 + (α + β)/2, then the (0,2)-interpolation problem is not regular. Recently, the author proved that for α, β both odd integers, the (0,2)-interpolation problem augmented with boundary (Hermite-type) conditions at the endpoints of the interval [−1,1] is regular. In this paper the convergence of this modified (0,2)-interpolation procedure is studied, if the inner nodal points are the roots of the ultraspherical polynomials with odd integer parameter.