TY  - JOUR
ID  - Cho2021
LB  - Cho2021
AU  - Cho, Ilwoo
AU  - Jorgensen, Palle E.T.
TI  - Multi-variable quaternionic spectral analysis
ST  - Multi-variable quaternionic spectral analysis
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2021
VL  - 41
IS  - 3
SP  - 335
EP  - 379
DO  - https://doi.org/10.7494/OpMath.2021.41.3.335
UR  - https://doi.org/10.7494/OpMath.2021.41.3.335
AB  - In this paper, we consider finite dimensional vector spaces \(\mathbb{H}^n\) over the ring \(\mathbb{H}\) of all quaternions. In particular, we are interested in certain functions acting on \(\mathbb{H}^n\), and corresponding functional equations. Our main results show that (i) all quaternions of \(\mathbb{H}\) are classified by the spectra of their realizations under representation, (ii) all vectors of \(\mathbb{H}^n\) are classified by a canonical extended setting of (i), and (iii) the usual spectral analysis on the matricial ring \(M_n(\mathbb{C})\) of all \((n \times n)\)-matrices over the complex numbers \(\mathbb{C}\) has close connections with certain "non-linear" functional equations on \(\mathbb{H}^n\) up to the classification of (ii).
KW  - the quaternions \(\mathbb{H}\)
KW  - vector spaces \(\mathbb{H}^n\) over \(\mathbb{H}\)
KW  - \(q\)-spectral forms
KW  - \(q\)-spectral functions
SN  - 1232-9274
ER  -