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.