Approximation of Hilbert and Hadamard transforms on (0,+∞)

The authors propose a numerical method for computing Hilbert and Hadamard transforms on (0,+∞) by a simultaneous approximation process involving a suitable Lagrange polynomial of degree s and “truncated” Gaussian rule of order m, with s≪m. The proposed procedure is convergent and pointwise error estimates are given. Finally, some numerical tests confirming the theoretical error estimates are presented.