Eigenfunctions corresponding to the band pass kernel with large center frequency

It is known that the eigenfunctions of the finite integral equation with band limited difference kernel are the prolate spheroidal wave functions. When the band pass difference kernel was considered, no such well-known functions were found, except for the limiting case of zero band width. In this report we show that for large values of the center frequency the eigenfunctions corresponding to the band pass kernel are related to the prolate spheroidal functions.