Lyapunov transformation of differential operators with unbounded operator coefficients

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• 作者：M. S. Bichegkuev
• 关键词：Lyapunov transformation ; evolution operator ; perturbed differential operator ; Cauchy problem ; Lyapunov kinematic similarity ; exponential dichotomy ; splitting pair of functions ; Bohl spectrum
• 刊名：Mathematical Notes
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：99
• 期：1-2
• 页码：24-36
• 全文大小：708 KB
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• 作者单位：M. S. Bichegkuev (1) (2)
  
  1. Khetagurov North-Ossetian State University, Vladikavkaz, Russia
  2. Gorskii State Agrarian University, Vladikavkaz, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1573-8876

文摘

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.