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 Mat. Zametki, 2016, Volume 99, Issue 1, Pages 11–25 (Mi mz10813)

Lyapunov Transformation of Differential Operators with Unbounded Operator Coefficients

M. S. Bichegkuevab

b Gorsky State Agricultural University, Vladikavkaz

Abstract: We introduce a number of notions related to the Lyapunov transformation of linear differential operators with unbounded operator coefficients generated by a family of evolution operators. We prove statements about similar operators related to the Lyapunov transformation and describe their spectral properties. One of the main results of the paper is a similarity theorem for a perturbed differential operator with constant operator coefficient, an operator which is the generator of a bounded group of operators. For the perturbation, we consider the operator of multiplication by a summable operator function. The almost periodicity (at infinity) of the solutions of the corresponding homogeneous differential equation is established.

Keywords: Lyapunov transformation, evolution operator, perturbed differential operator, Cauchy problem, Lyapunov kinematic similarity, exponential dichotomy, splitting pair of functions, Bohl spectrum.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-0019716-01-00212 Russian Science Foundation 14-21-00066

DOI: https://doi.org/10.4213/mzm10813

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English version:
Mathematical Notes, 2016, 99:1, 24–36

Bibliographic databases:

UDC: 517.984+517.983.28
Revised: 15.09.2015

Citation: M. S. Bichegkuev, “Lyapunov Transformation of Differential Operators with Unbounded Operator Coefficients”, Mat. Zametki, 99:1 (2016), 11–25; Math. Notes, 99:1 (2016), 24–36

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz10813
• https://doi.org/10.4213/mzm10813
• http://mi.mathnet.ru/eng/mz/v99/i1/p11

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. S. Bichegkuev, “Almost periodic at infinity solutions to integro-differential equations with non-invertible operator at derivative”, Ufa Math. J., 12:1 (2020), 3–12
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