Multi-variable quaternionic spectral analysis

Quaternionic Analysis

1. Introduction. The richness of the theory of functions over the complex field makes it natural to look for a similar theory for the only other non-trivial real asso-ciative division algebra, namely the quaternions. Such a theory exists and is quite far-reaching, yet it seems to be little known. It was not developed until nearly a century after Hamilton's discovery of quaternions. Hamilton him...

On quaternionic functional analysis

In this article, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion B∗-algebras are equivalent to the category of real vector spaces, the category of real Hilbert spaces and the category of real C∗-algebras respectively. We will also give a Riesz representation theorem for quaternion...

Multi-Image Unsupervised Spectral Analysis

Large data sets delivered by imaging spectrometers are interesting in many ways in the Planetary Sciences. Due to the size of the data, which often prohibits conventional exploratory data analysis, unsupervised analysis methods could be a way of gathering interesting information contained in the data. In this work, we investigate some of the opportunities and limitations of unsupervised analysi...

Depth analysis of Midway Atoll using Quickbird multi-spectral imaging over variable substrates

Extension results for slice regular functions of a quaternionic variable

In this paper we prove a new representation formula for slice regular functions, which shows that the value of a slice regular function f at a point q = x + yI can be recovered by the values of f at the points q + yJ and q + yK for any choice of imaginary units I, J,K. This result allows us to extend the known properties of slice regular functions defined on balls centered on the real axis to a...