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)-dim ensional sphere and show that, in the limit, as the points coalesce under a n angular scaling, the Lebesgue function of the process converges to that o f an associated algebraic interpolation problem for the original angles con sidered as points in Rd-1. (C) 1999 Academic Press.