Smooth Wavelets on the Sphere

In this paper a construction of C 1-wavelets on the two-dimensional sphere is presented. First, we focus on the construction of a multiresolution analysis leading to C 1-functions on S 2. We show reenablility of the constructed tensor product generators. Secondly, for the wavelet construction we employ a factorization of the reenement matrices which leads to reenement matrices characterizing complement spaces. With this method we achieve an initial stable completion. A desired stable completion can be gained by 'lifting' the initial stable completion according to the method of Carnicer, Dahmen and Pena 4]. The result ist a biorthogonal wavelet basis leading to C 1-functions on the sphere.