Radial Multiresolution in Dimension Three

We present a construction of a wavelet-type orthonormal basisfor the space of radial $L^2$-functions in {bf R}$^3$ via the concept of a radial multiresolution analysis. The elements of the basis are obtained from a singleradial wavelet by usual dilations and generalized translations. Hereby the generalized translation reveals the group convolution of radial functions in {bf R}$^3$. We provide a simple way to construct a radial scaling function and a radial waveletfrom an even classical scaling function on {bf R}. Furthermore, decomposition and reconstruction algorithms are formulated.