The Bergman Kernels for the half-ball and for fractional wedge-shaped domains in Clifford Analysis

Abstract

We compute the Bergman reproducing kernel for monogenic functions for half-ball, more general orthogonal ball sectors, and for fractional wedge domains. In the results we obtain the terms to be expected from analogy with complex analysis, viz in the first case the Bergman kernels for the half-space and the entire ball, and in the second the sum of rotated half-space Bergman kernels, but in both cases there also occur supplementary, purely hypercomplex correction terms. Finally, applying a periodisation argument we obtain closed and explicit formulas for the Bergman kernels of wedge shaped domains that are rectangularly bounded.