First order linear ordinary differential equations in associative algebras
| dc.contributor.author | Erlebacher, Gordon | |
| dc.contributor.author | Sobczyk, Garret E. | |
| dc.date.accessioned | 2021-04-05T13:52:14Z | |
| dc.date.available | 2021-04-05T13:52:14Z | |
| dc.date.issued | 2004-01-02 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 18 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13320 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2004, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Associate algebra | |
| dc.subject | Factor ring | |
| dc.subject | Idempotent | |
| dc.subject | Differential equations | |
| dc.subject | Nilpotent | |
| dc.subject | Spectral basis | |
| dc.subject | Toeplitz matrix | |
| dc.title | First order linear ordinary differential equations in associative algebras | |
| dc.type | Article |