Filtered integration rules for finite weighted Hilbert transforms II

TitleFiltered integration rules for finite weighted Hilbert transforms II
Publication TypeJournal Article
Year of Publication2022
AuthorsOccorsio, D, Russo, MG, Themistoclakis, W
JournalDolomites Research Notes on Approximation
Date Published10/2022
PublisherPadova University Press
Place PublishedPadova, IT
ISSN Number2035-6803

This paper is the continuation of a previous work where the authors have introduced a new class of quadrature rules for evaluating the finite Hilbert transform. Such rules are product type formulae based on the filtered de la Vallée Poussin (shortly VP) type approximation. Here, we focus on some particular cases of interest in applications and show that further results can be obtained in such special cases. In particular, we consider an optimal choice of the quadrature nodes for which explicit formulae of the quadrature weights are given and sharper error estimates are stated.