On Cauchy-Szeg\"o kernel for quaternionic Siegel upper half space

TL;DR

This paper constructs the Cauchy-Szeg"o kernel for quaternionic Hardy spaces, enabling integral representations of boundary functions in quaternionic analysis.

Contribution

It introduces a new Cauchy-Szeg"o kernel for quaternionic Siegel upper half space, extending classical complex analysis to quaternionic settings.

Findings

Established the Cauchy-Szeg"o kernel for quaternionic Hardy spaces.

Proved the kernel's properties and its role in boundary value problems.

Extended integral operator techniques to quaternionic analysis.

Abstract

The work is dedicated to the construction of the Cauchy-Szeg\"o kernel for the Cauchy-Szeg\"o projection integral operator from the space of $L^2$-integrable functions defined on the boundary of the quaternionic Siegel upper half space to the space of boundary values of the quaternionic regular functions of the Hardy space over the quaternionic Siegel upper half space.