A multivariate version of the disk convolution (Q892351)

The authors obtain a product formula for the spherical functions of the compact Gelfand pairs \((SU(p+q), SU(p) \times SU(q))\) with \(p\geq 2q\). These functions are expressed in terms of Heckman-Opdam Jacobi polynomials of type \(BC_q\). Extended product formulas for a continuous range of parameters \(p\in [2q -1, \infty[\) are obtained by analytic continuation using Carlson's theorem. The results of the paper extend known fact for the disk convolutions to the higher rank case.