1. Lyapunov transformation of differential operators with unbounded operator coefficients.
- Author
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Bichegkuev, M.
- Subjects
- *
LYAPUNOV functions , *DIFFERENTIAL operators , *PERTURBATION theory , *DIFFERENTIAL equations , *MATHEMATICS theorems - 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 ofmultiplication by a summable operator function. The almost periodicity (at infinity) of the solutions of the corresponding homogeneous differential equation is established. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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