关于位场频率域表示的一个理论问题

本文主要指出B.K.Bhattacharyya和M.E.Navolio在文献[1]中将拉普拉斯方程▽2U（x,y,z）=0进行三维傅里叶变换导出u2+v2+w2=0,以及利用iw=±（u2+v2）1/2推导了位场在频率域中的一些公式中的错误,从数学和物理角度论证这个所谓频率域的拉普拉斯方程u2+v2+w2=0是不成立的。因此,当推导位场在频率域中的公式时不能使用iw=±（u2+v2）1/2。此外,本文还使用狄拉克函数证明了拉普拉斯方程的基本解1/（x2+y2+z2）1/2在拉普拉斯算子作用下,在三维频率域中并没有这样的对应关系式,而只能有对应关系式

A THEORETICAL PROBLEM CONCERNING THE FREQUENCY DOMAIN REPRESENTATION OF THE POTENTIAL FIELD

In 1976 B. K. Bhattacharyya and M. E. Navolio made a three-dimensional Fourier transform on Laplace equation ▽2u（x,y,z）=0 and led to the equation u2 + v2 + w2=0[1]. Then they deduced some formulae of potential field in the frequency domain from theformula iw =±u2 + v2.In this paper it is demonstrated that the so-called Laplace equation in the frequency domain u2+v2+w2=0 is invalid and,consequently,iw=±u2+v2 can not be used to deduce the frequency domain representation of potential field. In addition,using Dirac delta function,it is shown that the corresponding relation to the element-ary solution of Laplace equation,1/（（x2+y2+z2）1/2）operated by Laplacian in the three-dimensional frequency domain ought to be （u2+v2+w2） T （u,v,w）=4π but not （u2+v2+w2）T（u,v,w）=0.