Abstract
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 ) ) .
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