Approximation of the Hilbert transform on (0, +∞) by using discrete de la Vallée Poussin filtered polynomials

In the present paper, is proposed a method to approximate the Hilbert transform of a given function f on (0, +∞) employing truncated de la Vallée discrete polynomials recently studied in [25]. The method generalizes and improves in some sense that introduced in [24] based on a truncated Lagrange interpolating polynomial, since is faster convergent and simpler to apply. Moreover, the additional parameter defining de la Vallée polynomials helps to attain better pointwise approximations. Stability and convergence are studied in weighted uniform spaces and some numerical tests are provided to asses the performance of the procedure.