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JOURNALS // Funktsional'nyi Analiz i ego Prilozheniya // Archive
Funktsional. Anal. i Prilozhen., 2023 Volume 57, Issue 4, Pages 130–132 (Mi faa4093)
This article is cited in 1 paper

Brief communications

The Cayley–Hamilton theorem and resolvent representation

I. D. Kostrub

Voronezh State University

Abstract: For the Frobenius matrix accompanying an algebraic (differential) equation in a complex Banach algebra, the Cayley–Hamilton theorem is proved, which is used to obtain a representation of the resolvent.

Keywords: complex Banach algebra, algebraic and differential equations, resolvent, accompanying Frobenius matrix, Cayley–Hamilton theorem.

Received: 06.02.2023
Revised: 25.05.2023
Accepted: 26.05.2023

DOI: 10.4213/faa4093


 English version: Functional Analysis and Its Applications, 2023, 57:4, 371–373

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© Steklov Math. Inst. of RAS, 2025