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.

UDC: 517.9

Received: 05.05.1997

DOI: 10.4213/mzm1016

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

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