The schoenflies extension in the analytic case

Summary Let S be an (n−1)-sphere in a euclidean n-space E. Let B be the closed n-ball in E bounded by S. Let z be an arbitrary point of . A real analytic diffeomorphism f of S into E admits a homeomorphic extension F which is defined over some open neighborhood N of B and such that F | (N−z) is an analytic diffeomorphism. We give a new proof of this theorem to serve as a model for a forthcoming theory of analytic families of such extensions. To Enrico Bompiani on his scientific Jubilee.