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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 491, Pages 73–77
DOI: https://doi.org/10.31857/S2686954320020174 (Mi danma53) 		 
This article is cited in 8 scientific papers (total in 8 papers)

MATHEMATICS

Differential equations in Banach algebras

A. I. Perov, I. D. Kostrub

Voronezh State University, Voronezh, Russian Federation
Full-text PDF (169 kB) Citations (8)
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DOI: https://doi.org/10.31857/S2686954320020174
Abstract: 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.
Funding agency Grant number
Russian Foundation for Basic Research 19–01–00732
This study was supported by the Russian Foundation for Basic Research, project no. 19-01-00732.
Presented: E. I. Moiseev
Received: 16.10.2019
Revised: 27.02.2020
Accepted: 27.02.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 2, Pages 139–143
DOI: https://doi.org/10.1134/S1064562420020179
Bibliographic databases:
Document Type: Article
UDC: 517.957
Language: Russian
Citation: A. I. Perov, I. D. Kostrub, “Differential equations in Banach algebras”, Dokl. RAN. Math. Inf. Proc. Upr., 491 (2020), 73–77; Dokl. Math., 101:2 (2020), 139–143
Citation in format AMSBIB
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\jour Dokl. Math.
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