The orthogonal projection on slice functions on the quaternionic sphere

TL;DR

This paper investigates the behavior of the orthogonal projection operator on quaternionic functions, focusing on its $L^p$ norm when projecting onto slice functions within quaternionic $L^2$ spaces.

Contribution

It provides new insights into the $L^p$ bounds of the orthogonal projection onto slice functions in quaternionic analysis.

Findings

Derived bounds for the $L^p$ norm of the projection

Characterized the projection's behavior on quaternionic $L^2$ spaces

Extended classical results to quaternionic slice functions

Abstract

We study the $L^p$ norm of the orthogonal projection from the space of quaternion valued $L^2$ functions to the closed subspace of slice $L^2$ functions.