Approximation of the Hilbert transform on $(0,+\\\\infty)$ by using discrete de la Vall`ee Poussin filtered polynomials

Authors : Donatella Occorsio

Pages : 114-128

Doi:10.33205/cma.1541668

View : 17 | Download : 19

Publication Date : 2024-12-16

Article Type : Research Paper

Abstract :In the present paper, is proposed a method to approximate the Hilbert transform of a given function $f$ on $(0,\\\\infty)$ employing truncated de la Vallée discrete polynomials recently studied in [25]. The method generalizes and improves in some sense a method based on truncated Lagrange interpolating polynomials introduced in [24], 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.
Keywords : Hilbert transform, discrete de la Vallée-Poussin approximation, Approximation by polynomials