A product quadrature rule, based on the filtered de la Vall\'ee Poussin polynomial approximation, is proposed for evaluating the finite 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.
翻译:为评价[1;1]中有限的Hilbert变形,提议了一种基于过滤法的产物二次曲线规则,用于评价[1;1]中有限的Hilbert变形。对属于合适的Besov类型子空间的函数,在加权统一规范中列出了相容结果。提供了若干数字测试,还将该规则与文献中的其他公式进行比较。