论文标题
希尔伯特变革的截断：独特性和Chebyshev系列扩展方法
Truncated Hilbert Transform: Uniqueness and a Chebyshev series Expansion Approach
论文作者
论文摘要
如果使用Sokhotski-plemelj公式在相同的间隔中知道具有紧凑的支持及其截断的希尔伯特变换的功能，我们将获得更强的唯一性结果。为了从其截断的Hilbert变换中找到一个函数，我们在Chebyshev多项式序列中表达它们，然后提出两种方法来估计系数。我们提出计算机模拟结果，以表明外推过程在数值上效果很好。
We derive a stronger uniqueness result if a function with compact support and its truncated Hilbert transform are known on the same interval by using the Sokhotski-Plemelj formulas. To find a function from its truncated Hilbert transform, we express them in the Chebyshev polynomial series and then suggest two methods to numerically estimate the coefficients. We present computer simulation results to show that the extrapolative procedure numerically works well.
