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Mat. Zametki, 2011, Volume 89, Issue 2, Pages 190–203 (Mi mz8634)  

This article is cited in 8 scientific papers (total in 8 papers)

Hyperbolic Operator Semigroups and Lyapunov's Equation

A. G. Baskakov, A. A. Vorobjev, M. Yu. Romanova

Voronezh State University

Abstract: We obtain necessary and sufficient conditions for the hyperbolicity of a semigroup of operators. In so doing, we use Lyapunov's equation in operator form constructed from its generator.

Keywords: hyperbolic semigroup of operators, Lyapunov's equation, exponential dichotomy, Howland hyperbolic semigroup, Banach algebra, Krein's theorem

DOI: https://doi.org/10.4213/mzm8634

Full text: PDF file (554 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2011, 89:2, 194–205

Bibliographic databases:

UDC: 517.984+517.986
Received: 17.02.2009

Citation: A. G. Baskakov, A. A. Vorobjev, M. Yu. Romanova, “Hyperbolic Operator Semigroups and Lyapunov's Equation”, Mat. Zametki, 89:2 (2011), 190–203; Math. Notes, 89:2 (2011), 194–205

Citation in format AMSBIB
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\paper Hyperbolic Operator Semigroups and Lyapunov's Equation
\jour Mat. Zametki
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\issue 2
\pages 190--203
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\crossref{https://doi.org/10.4213/mzm8634}
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\yr 2011
\vol 89
\issue 2
\pages 194--205
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  • http://mi.mathnet.ru/eng/mz/v89/i2/p190

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Romanovskii R.K., Nazaruk E.M., “Spektralnyi kriterii eksponentsialnoi dikhotomii dlya lineinoi avtonomnoi sistemy funktsionalno-differentsialnykh uravnenii”, Doklady Akademii nauk vysshei shkoly Rossiiskoi Federatsii, 2012, no. 1, 19–27  elib
    2. M. Yu. Romanova, “O chislovoi oblasti generatora polugruppy”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 12:1 (2012), 29–32  mathnet  crossref  elib
    3. A. G. Baskakov, “Analysis of linear differential equations by methods of the spectral theory of difference operators and linear relations”, Russian Math. Surveys, 68:1 (2013), 69–116  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. A. G. Chshiev, “The Gearhart–Prüss Theorem for a Class of Degenerate Semigroups of Operators”, Math. Notes, 94:3 (2013), 400–413  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Yu. F. Dolgii, “Vychislenie kvadratichnykh funktsionalov Lyapunova–Krasovskogo dlya lineinykh avtonomnykh sistem s posledeistviem”, Tr. IMM UrO RAN, 19, no. 4, 2013, 95–106  mathnet  mathscinet  elib
    6. R. K. Romanovskii, E. M. Nazaruk, “On the Dichotomy of Linear Autonomous Systems of Functional-Differential Equations”, Math. Notes, 95:1 (2014), 116–121  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. A. G. Baskakov, “Estimates for the Green's function and parameters of exponential dichotomy of a hyperbolic operator semigroup and linear relations”, Sb. Math., 206:8 (2015), 1049–1086  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. A. G. Baskakov, D. M. Polyakov, “The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential”, Sb. Math., 208:1 (2017), 1–43  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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