Complex Variables: Theory and Application vol:47 issue:4 pages:349-360
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 Szeg\"o 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 Szeg\"o 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.