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....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.展开更多
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.
文摘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.
