期刊
MATHEMATICS OF COMPUTATION
卷 80, 期 275, 页码 1745-1767出版社
AMER MATHEMATICAL SOC
DOI: 10.1090/S0025-5718-2011-02418-X
关键词
Cauchy transform; Cauchy principal value integrals; Hilbert transform; Riemann-Hilbert problems; singular integral equations; quadrature
We construct a new method for approximating Hilbert transforms and their inverse throughout the complex plane. Both problems can be formulated as Riemann-Hilbert problems via Plemelj's lemma. Using this framework, we rederive existing approaches for computing Hilbert transforms over the real line and unit interval, with the added benefit that we can compute the Hilbert transform in the complex plane. We then demonstrate the power of this approach by generalizing to the half line. Combining two half lines, we can compute the Hilbert transform of a more general class of functions on the real line than is possible with existing methods.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据