Szegö and Polymonogenic Bergman Kernels for Half-Space and Strip Domains, and Single-Periodic Functions in Clifford Analysis

Abstract

In this paper, we consider half-space domains (semi-infinite in one of the dimensions) and strip domains (finite in one of the dimensions) in real Euclidean spaces of dimension at least 2. The Szegö reproducing kernel for the space of monogenic and square integrable functions on a strip domain is obtained in closed form as a monogenic single-periodic function, viz a monogenic cosecant. The relationship between the Szegö and Bergman kernel for monogenic functions in a strip domain is explicitated in the transversally Fourier transformed setting. This relationship is then generalised to the polymonogenic Bergman case. Finally, the half-space case is considered specifically and the simplifications are pointed out.