The Quaternionic Cauchy-Szeg\"{o} Kernel on the Quaternionic Siegel Half Space

TL;DR

This paper derives the quaternionic Cauchy-Szeg"{o} kernel for Hardy spaces on the quaternionic Siegel half space and explores analogous structures in the octonionic setting.

Contribution

It provides the explicit form of the quaternionic Cauchy-Szeg"{o} kernel and investigates Hardy spaces on the octonionic Siegel half space, extending classical analysis to quaternionic and octonionic contexts.

Findings

Explicit quaternionic Cauchy-Szeg"{o} kernel derived

Hardy spaces on quaternionic and octonionic Siegel half spaces studied

Extension of classical analysis to quaternionic and octonionic settings

Abstract

The quaternionic Cauchy-Szeg\"{o} kernel of the Hardy space $\mathcal{H}^2(\mathcal{U}_n)$ on the quaternionic Siegel half space $\mathcal{U}_n$ is derived and the Hardy spaces on the octonionic Siegel half space is investigated.