Gordon Erlebacher & Garrret E. Sobczyk
In this paper, we study the linear differential equation
in an associative but non-commutative algebra , where the form a set of commuting -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.
Submitted September 6, 2003. Published January 2, 2004.
Math Subject Classifications: 15A33, 15A66, 34G10, 39B12.
Key Words: Associative algebra, factor ring, idempotent, differential equation, nilpotent, spectral basis, Toeplitz matrix.
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| Gordon Erlebacher |
Department of Mathematics
Florida State University
Tallahassee, FL 32306, USA
| Garret E. Sobczyk |
Universidad de las Americas
Departamento de Fisico-Matematicas
Apartado Postal #100, Santa Catarina Martir
72820 Cholula, Pue., Mexico
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