title: On the compactness of solutions to certain operator inequalities arising from the Likhtarnikov — Yakubovich frequency theorem
metadata.name: dc.contributor.author
metadata.value: Anikushin, Mikhail M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-12-18T16:48:48Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-12-18T16:48:48Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Anikushin M. On the compactness of solutions to certain operator inequalities arising from the Likhtarnikov — Yakubovich frequency theorem. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 4, pp. 622–635
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2020.405
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/21846
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We study the compactness property of operator solutions to certain operator inequalities
  arising from the frequency theorem of Likhtarnikov — Yakubovich for C0-semigroups. We
  show that the operator solution can be described through solutions of an adjoint problem as
  it was previously known under some regularity condition. Thus we connect some regularity
  properties of the semigroup with the compactness of the operator in the general case. We
  also prove several results useful for checking the non-compactness of operator solutions to
  Lyapunov inequalities and equations, into which the operator Riccati equation degenerates
  in certain cases arising in applications. As an example, we apply these theorems for a scalar
  delay equation posed in a proper Hilbert space and show that the operator solution cannot
  be compact. This results are related to the author recent work on a non-local reduction
  principle of cocycles (non-autonomous dynamical systems) in Hilbert spaces.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work is supported by V. A. Rokhlin grant for young mathematicians of Saint Petersburg.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: frequency theorem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lyapunov inequality
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: compact operator
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: delay equations
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the compactness of solutions to certain operator inequalities arising from the Likhtarnikov — Yakubovich frequency theorem
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 622-635.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/21846/1/622-635.pdf
resources.format: Adobe PDF
resources.size: 345,77 kB