Integral Equations for the Spin-Weighted Spheroidal Wave Functions  

作　　者：田贵花 

机构地区：[1]School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 [2]Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080

出　　处：《Chinese Physics Letters》2005年第12期3013-3016,共4页中国物理快报（英文版）

基　　金：Supported by the National Natural Science Foundations of China under Grant Nos 10475013, 10373003, 10375087, and 10375008, the National Basic Research Program under Grant No 2004CB318000, and the Post-Doctor Foundation of China.

摘　　要：We present new integral equations for the spin-weighted spheroidal wave functions which in turn should lead to global uniform estimates and should help in particular in the study of their dependence on the parameters. For the prolate spheroidal wavefunction with m=0, there exists the integral equation whose kernel is （sin x）/x, and the sinc function kernel （sin x）/x is of great mathematical significance. We also extend the similar sinc function kernel （sin x）/x to the case m≠0 and s≠0, which interestingly turn out as some kind of Hankel transformations.We present new integral equations for the spin-weighted spheroidal wave functions which in turn should lead to global uniform estimates and should help in particular in the study of their dependence on the parameters. For the prolate spheroidal wavefunction with m=0, there exists the integral equation whose kernel is （sin x）/x, and the sinc function kernel （sin x）/x is of great mathematical significance. We also extend the similar sinc function kernel （sin x）/x to the case m≠0 and s≠0, which interestingly turn out as some kind of Hankel transformations.

关 键 词：ROTATING BLACK HOLE FOURIER-ANALYSIS STABILITY PERTURBATIONS 

分 类 号：P145.8[天文地球—天体物理]