Interpolation a plusieurs variables sur la sphere

Summary Given a functionf defined on the sphere , a continuation is considered which transformsf into a periodic function with period 2, accordingto each of the two usual variables , .Starting from this continuation, an explicit interpolation formula forf on in a set of trigonometric functions is obtained. A simple and numerically stable quadrature formula is given, which is accurate for a vast class of functions.Error-bounds for approximation and quadrature are given.