First order linear ordinary differential equations in associative algebras
Date
2004-01-02
Authors
Erlebacher, Gordon
Sobczyk, Garret E.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
In this paper, we study the linear differential equation
dx/ dt = Σni=1 ai(t)xbi(t) + ƒ(t)
in an associative but non-commutative algebra A, where the bi(t) form a set of commuting A-valued functions expressed in a time-independent spectral basis consisting of mutually annihilating idempotents and nilpotents. Explicit new closed solutions are derived, and examples are presented to illustrate the theory.
Description
Keywords
Associate algebra, Factor ring, Idempotent, Differential equations, Nilpotent, Spectral basis, Toeplitz matrix
Citation
Erlebacher, G., & Sobczyk, G. E. (2004). First order linear ordinary differential equations in associative algebras. <i>Electronic Journal of Differential Equations, 2004</i>(1), pp. 1-18.
Rights
Attribution 4.0 International