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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2000, Volume 68, Issue 6, Pages 935–938 (Mi mz1016)

An Analog of the Cameron–Johnson Theorem for Linear $\mathbb C$-Analytic Equations in Hilbert Space

D. N. Cheban

Moldova State University

Abstract: The well-known Cameron–Johnson theorem asserts that the equation $\dot x=\mathcal A(t)x$ with a recurrent (Bohr almost periodic) matrix $\mathcal A(t)$ can be reduced by a Lyapunov transformation to the equation $\dot y=\mathcal B(t)y$ with a skew-symmetric matrix $\mathcal B(t)$, provided that all solutions of the equation $\dot x=\mathcal A(t)x$ and of all its limit equations are bounded on the whole line. In the note, a generalization of this result to linear $\mathbb C$-analytic equations in a Hilbert space is presented.

DOI: https://doi.org/10.4213/mzm1016

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English version:
Mathematical Notes, 2000, 68:6, 790–793

Bibliographic databases:

UDC: 517.9

Citation: D. N. Cheban, “An Analog of the Cameron–Johnson Theorem for Linear $\mathbb C$-Analytic Equations in Hilbert Space”, Mat. Zametki, 68:6 (2000), 935–938; Math. Notes, 68:6 (2000), 790–793

Citation in format AMSBIB
\Bibitem{Che00}
\by D.~N.~Cheban
\paper An Analog of the Cameron--Johnson Theorem for Linear $\mathbb C$-Analytic Equations in Hilbert Space
\jour Mat. Zametki
\yr 2000
\vol 68
\issue 6
\pages 935--938
\mathnet{http://mi.mathnet.ru/mz1016}
\crossref{https://doi.org/10.4213/mzm1016}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1835192}
\zmath{https://zbmath.org/?q=an:1001.34078}
\transl
\jour Math. Notes
\yr 2000
\vol 68
\issue 6
\pages 790--793
\crossref{https://doi.org/10.1023/A:1026621019011}