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dc.contributor.authorErlebacher, Gordon ( )
dc.contributor.authorSobczyk, Garret E. ( Orcid Icon 0000-0002-8023-9593 )
dc.date.accessioned2021-04-05T13:52:14Z
dc.date.available2021-04-05T13:52:14Z
dc.date.issued2004-01-02
dc.identifier.citationErlebacher, G., & Sobczyk, G. E. (2004). First order linear ordinary differential equations in associative algebras. Electronic Journal of Differential Equations, 2004(1), pp. 1-18.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13320
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.formatText
dc.format.extent18 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2004, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectAssociate algebraen_US
dc.subjectFactor ringen_US
dc.subjectIdempotenten_US
dc.subjectDifferential equationsen_US
dc.subjectNilpotenten_US
dc.subjectSpectral basisen_US
dc.subjectToeplitz matrixen_US
dc.titleFirst order linear ordinary differential equations in associative algebrasen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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