Approximation of the Hilbert transform on the half–line

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-07-18 DOI:10.1016/j.apnum.2024.07.004

Donatella Occorsio , Woula Themistoclakis

引用次数: 0

Abstract

The paper concerns the weighted Hilbert transform of locally continuous functions on the semiaxis. By using a filtered de la Vallée Poussin type approximation polynomial recently introduced by the authors, it is proposed a new “truncated” product quadrature rule (VP- rule). Several error estimates are given for different smoothness degrees of the integrand ensuring the uniform convergence in Zygmund and Sobolev spaces. Moreover, new estimates are proved for the weighted Hilbert transform and for its approximation (L-rule) by means of the truncated Lagrange interpolation at the same Laguerre zeros. The theoretical results are validated by the numerical experiments that show a better performance of the VP-rule versus the L-rule.

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半线上的希尔伯特变换近似值

本文涉及半轴上局部连续函数的加权希尔伯特变换。通过使用作者最近引入的滤波 de la Vallée Poussin 型逼近多项式，提出了一种新的 "截断 "乘积正交规则（VP- 规则）。针对积分的不同平滑度，给出了若干误差估计值，以确保在齐格蒙特空间和索博列夫空间的均匀收敛。此外，还证明了加权希尔伯特变换的新估计值，以及通过在相同的拉盖尔零点进行截断拉格朗日插值对其近似（L-规则）的新估计值。数值实验验证了这些理论结果，实验结果表明 VP 规则与 L 规则相比具有更好的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.