摘要
零阶角长球面波函数在信号处理等中有着重要应用。它可由积分方程来定义；亦可由求解其微分方程得到。本文利用斯图谟－刘维尔问题．积分方程中希尔伯特－施密特理论，积分变换的正交不变性及δ函数的性质，首次从数学上给出了这种函数微分方程与积分方程等价关系的一般证明。
The prolate spheroidal wave functions have been widely used in electroma- gnetic propagation and signal processing, etc.. In practice, angular prolate spheroidal wave functions of zero order are particularly useful. The angular prolate spheroidal wave function of zero order can be obtained by solving its differential equation or integral equation. Up to now, the proof of the equivalent relation of integral equation and differential equation of angular prolate spheroidal wave function is not given. This paper, for the first time, shows that the integral equation is equivalent to the differential equation of angular prolate spheroidal wave function of zero order by means of the problems of Sturm-Liouville, Hibert- Schmidt's theory in integral equation, the orthogonal invariance of integral transforms and the properties of Dirac δ function.
出处
《大连理工大学学报》
EI
CAS
CSCD
北大核心
1991年第2期223-226,共4页
Journal of Dalian University of Technology
关键词
球面波
球函数
微分方程
积分方程
spheroidal waves
spheroidal function
differential equation
integral equation/angular prolate spheroidal wave functions of zero order
