Geodesic
On differential equations in Banach algebras
Vestnik rossijskih universitetov. Matematika, Tome 25 (2020) no. 132, pp. 410-421
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We consider higher-order linear differential equations with constant coefficients in Banach algebras (this is a direct generalization of higher-order matrix differential equations). The presentation is based on higher algebra, differential equations and functional analysis. The results obtained can be used in the study of matrix equations, in the theory of small oscillations in physics, and in the theory of perturbations in quantum mechanics. The presentation is based on the original research of the authors.
Keywords: higher-order differential equations, Banach algebras, Sylvester's theorem, Hilbert identity, Cauchy function, non-resonant condition and frequency constants, bounded green function and integral constants, non-commutative Viet formula. 
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A. I. Perov; I. D. Kostrub. On differential equations in Banach algebras. Vestnik rossijskih universitetov. Matematika, Tome 25 (2020) no. 132, pp. 410-421. http://geodesic.mathdoc.fr/item/VTAMU_2020_25_132_a5/

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