Multivariate Lagrange interpolation and polynomials of one quaternionic variable

TL;DR

This paper extends classical Lagrange interpolation to polynomials of a quaternionic variable, developing the theory and proposing multivariate interpolation schemes with favorable geometric properties for real and complex spaces.

Contribution

It introduces the theory of quaternionic polynomials and develops multivariate interpolation schemes with geometric advantages for real and complex spaces.

Findings

Developed the theory of quaternionic polynomials

Proposed multivariate interpolation schemes with good geometric properties

Explored least and Kergin interpolation in this context

Abstract

This paper considers the extension of classical Lagrange interpolation in one real or complex variable to "polynomials of one quaternionic variable". To do this we develop some aspects of the theory of such polynomials. We then give a number of related multivariate polynomial interpolation schemes for ${\mathbb{R}}^4$ and ${\mathbb{C}}^2$ with good geometric properties, and some aspects of least interpolation and of Kergin interpolation.