Lagrange Interpolation with Constraints on the Real Line

We investigate the uniform convergence of Lagrange interpolation at the zeros of the orthogonal polynomials with respect to a Freud-type weight in the presence of constraints. We show that by a simple procedure it is always possible to transform the matrices of these zeros into matrices such that the corresponding Lagrange interpolating polynomial with re- spect to the given constraints well approximates a given function. This procedure was, at ¯rst, successfully introduced for the polynomial inter- polation with constraints on bounded intervals [1]. For this procedure we obtain the same results obtained in [10], where only the zeros of the orthogonal polynomials are used.