Geodesic
Differential equations in Banach algebras
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 73-77.

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In a complex Banach algebra that is not assumed to be commutative, $n$th-order linear differential equations with constant coefficients are considered. The corresponding algebraic characteristic equation of the $n$th degree is assumed to have $n$ distinct roots for which the Vandermonde matrix is invertible. Analogues of Sylvester's and Vieta's theorems are proved, and a contour integral of Cauchy type is studied.
Keywords: Banach algebra, higher order differential equations, algebraic characteristic equation, Vandermonde matrix, Sylvester's and Vieta's theorems, Cauchy-type contour integral. 
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A. I. Perov; I. D. Kostrub. Differential equations in Banach algebras. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 73-77. http://geodesic.mathdoc.fr/item/DANMA_2020_491_a14/

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