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Lyapunov transformation of differential operators with unbounded operator coefficients.
- Source :
- Mathematical Notes; Jan2016, Vol. 99 Issue 1/2, p24-36, 13p
- Publication Year :
- 2016
-
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]
Details
- Language :
- English
- ISSN :
- 00014346
- Volume :
- 99
- Issue :
- 1/2
- Database :
- Complementary Index
- Journal :
- Mathematical Notes
- Publication Type :
- Academic Journal
- Accession number :
- 114078200
- Full Text :
- https://doi.org/10.1134/S000143461601003X