Reproducing Kernels and Conformal Mappings in

In this paper we look at the theory of reproducing kernels for spaces of functions in a Clifford algebra _{0, n}. A first result is that reproducing kernels of this kind are solutions to a minimum problem, which is a non-trivial extension of the analogous property for real and complex valued functions. In the next sections we restrict our attention to Szegö and Bergman modules of monogenic functions. The transformation property of the Szegö kernel under conformal transformations is proved, and the Szegö and Bergman kernels for the half space are calculated.