Geodesic
An Analog of the Cameron--Johnson Theorem for Linear $\mathbb C$-Analytic Equations in Hilbert Space
Matematičeskie zametki, Tome 68 (2000) no. 6, pp. 935-938.

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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. 
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     title = {An {Analog} of the {Cameron--Johnson} {Theorem} for {Linear} $\mathbb C${-Analytic} {Equations} in {Hilbert} {Space}},
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D. N. Cheban. An Analog of the Cameron--Johnson Theorem for Linear $\mathbb C$-Analytic Equations in Hilbert Space. Matematičeskie zametki, Tome 68 (2000) no. 6, pp. 935-938. http://geodesic.mathdoc.fr/item/MZM_2000_68_6_a13/

[1] Cameron R. H., “Almost periodic properties of bounded solutions of linear differential equations with almost periodic coefficients”, J. Math. Phys., 15 (1936), 73–81 | Zbl

[2] Johnson R. A., “On a Floquet theory for almost periodic, two-dimensional linear systems”, J. Differential Equations, 37 (1980), 184–205 | DOI | MR | Zbl

[3] Koddington E. A., Levinson N., Teoriya obyknovennykh differentsialnykh uravnenii, Mir, M., 1958

[4] Demidovich B. P., Lektsii po matematicheskoi teorii ustoichivosti, Nauka, M., 1967

[5] Daletskii Yu. L., Krein M. G., Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nauka, M., 1970

[6] Shvarts L., Analiz, T. 2, Mir, M., 1973

[7] Burbaki N., Topologicheskie vektornye prostranstva, Mir, M., 1959

[8] Rudin U., Funktsionalnyi analiz, Mir, M., 1975

[9] Khalmosh P., Gilbertovo prostranstvo v zadachakh, Mir, M., 1970 | Zbl

[10] Scherbakov B. A., Ustoichivost po Puassonu dvizhenii dinamicheskikh sistem i reshenii differentsialnykh uravnenii, Shtiintsa, Kishinev, 1985