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Multi-variable quaternionic spectral analysis

Cho Ilwoo, Jorgensen Palle E. T.

Opuscula Mathematica

2021

Vol. 41, no. 3

In this paper, we consider finite dimensional vector spaces Hn over the ring H of all quaternions. In particular, we are interested in certain functions acting on Hn , and corresponding functional equations. Our main results show that (i) all quaternions of H are classified by the spectra of their realizations under representation, (ii) all vectors of Hn are classified by a canonical extended setting of (i), and (iii) the usual spectral analysis on the matricial ring Mn (C) of all (n x n)-matrices over the complex numbers C has close connections with certain “non-linear” functional equations on Hn up to the classification of (ii).