New Algorithm for Solving Non-linear Functional Equations

2020 ◽  
Vol 6 (2) ◽  
Author(s):  
Manoj Kumar ◽  
Aman Jhinga ◽  
Varsha Daftardar-Gejji
Keyword(s):  
Functional Equations ◽  
Linear Functional ◽  
Linear Functional Equations ◽  
Non Linear

scholarly journals Multi-variable quaternionic spectral analysis

2021 ◽  
Vol 41 (3) ◽  
pp. 335-379
Author(s):  
Ilwoo Cho ◽  
Palle E.T. Jorgensen
Keyword(s):  
Spectral Analysis ◽  
Functional Equations ◽  
Linear Functional ◽  
Vector Spaces ◽  
Complex Numbers ◽  
Dimensional Vector ◽  
Finite Dimensional ◽  
Linear Functional Equations ◽  
Non Linear

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).

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