Geodesic
Lyapunov Transformation of Differential Operators with Unbounded Operator Coefficients
Matematičeskie zametki, Tome 99 (2016) no. 1, pp. 11-25

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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. 
@article{MZM_2016_99_1_a1,
     author = {M. S. Bichegkuev},
     title = {Lyapunov {Transformation} of {Differential} {Operators} with {Unbounded} {Operator} {Coefficients}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {11--25},
     publisher = {mathdoc},
     volume = {99},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_1_a1/}
}
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M. S. Bichegkuev. Lyapunov Transformation of Differential Operators with Unbounded Operator Coefficients. Matematičeskie zametki, Tome 99 (2016) no. 1, pp. 11-25. http://geodesic.mathdoc.fr/item/MZM_2016_99_1_a1/