Lagrange Interpolation with Constraints on the Zeros of Hermite Polynomials

We investigate the uniform convergence of Lagrange interpolation at the zeros of Hermite polynomials 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 respect to the given constraints well approximates a given function. This procedure was, at first, successfully introduced for the polynomial interpolation with constraints on bounded intervals [1]. For this procedure we obtain the same results obtained in [2], where only the zeros of the Hermite polynomial are used.