Limiting values under scaling of the Lebesgue function for polynomial interpolation on spheres

We consider interpolation by spherical harmonics at points on a (d - 1)-dimensional sphere and show that, in the limit, as the points coalesce under an angular scaling, the Lebesgue function of the process converges to that of an associated algebraic interpolation problem for the original angles considered as points in Rd-1. (C) 1999 Academic Press.