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. 
@article{DANMA_2020_491_a14,
     author = {A. I. Perov and I. D. Kostrub},
     title = {Differential equations in {Banach} algebras},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {73--77},
     publisher = {mathdoc},
     volume = {491},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_491_a14/}
}
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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/