Christoffel–Darboux formula for zonal spherical functions for the Gelfand pair (U(n),U(n−1))

In this paper, first we show that an analogy of the Christoffel–Darboux formula holds for the zonal spherical functions for the Gelfand pair (U(n),U(n−1)). Next, making use of it, we deal with the problem on point-wise convergence of Fourier expansion by means of the zonal spherical functions for (U(n),U(n−1)).