A method to evaluate the Hilbert transform on (0, +∞)

摘要

The author proposes a method to approximate the Hilbert transform on the real positive semiaxis by a suitable Lagrange interpolating polynomial. The method employs truncated Gaussian rules and uses the interlacing properties of the zeros of generalized Laguerre polynomials. The error estimate in a weighted uniform norm is proved and some numerical tests show the efficacy of the proposed procedure.