Abstract
The well-known Cameron--Johnson theorem asserts that the equation \(\dot x = \mathcal{A}\left( t \right)x\) with a recurrent (Bohr almost periodic) matrix \(\mathcal{A}\left( t \right)\) can be reduced by a Lyapunov transformation to the equation \(\dot y = \mathcal{B}\left( t \right)y\) with a skew-symmetric matrix \(\mathcal{B}\left( t \right)\), provided that all solutions of the equation \(\dot x = \mathcal{A}\left( t \right)x\) 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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Cheban, D.N. An Analog of the Cameron--Johnson Theorem for Linear ℂ-Analytic Equations in Hilbert Space. Mathematical Notes 68, 790–793 (2000). https://doi.org/10.1023/A:1026621019011
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DOI: https://doi.org/10.1023/A:1026621019011