A product quadrature rule, based on the filtered de la Vallée Poussin polynomial approximation, is proposed for evaluating the finite weighted Hilbert transform in [−1,1]. Convergence results are stated in weighted uniform norm for functions belonging to suitable Besov-type subspaces. Several numerical tests are provided, also comparing the rule with other formulas known in literature.
Filtered integration rules for finite weighted Hilbert transforms
Occorsio D.;Russo M. G.;
2022-01-01
Abstract
A product quadrature rule, based on the filtered de la Vallée Poussin polynomial approximation, is proposed for evaluating the finite weighted Hilbert transform in [−1,1]. Convergence results are stated in weighted uniform norm for functions belonging to suitable Besov-type subspaces. Several numerical tests are provided, also comparing the rule with other formulas known in literature.File in questo prodotto:
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