Abstract
We present a classification of canonical systems and show that, under certain conditions, Hamiltonians belonging to the same class are linearly similar.
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References
L. A. Sakhnovich, “Problems of factorization and operator identities,”Usp. Mat. Nauk,41, No. 1, 3–55 (1986).
I. Ts. Gokhberg and M. G. Krein,Theory of the Volterra Operators in Hilbert Spaces and Its Applications [in Russian], Nauka, Moscow (1967).
L. A. Sakhnovich, “Equations with difference kernels on a system of segments,”Teor. Funkts., Funkts. Anal. Prilozhen., Issue 45, 111–122 (1986).
N. K. Bari,Trigonometric Series [in Russian], Fizmatgiz, Moscow (1961).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1428–1431, October, 1994.
The work was partially supported by the Ukrainian State Committee on Science and Technology.
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Sakhnovich, L.A. On a hypothesis concerning Hamiltonians of canonical systems. Ukr Math J 46, 1578–1583 (1994). https://doi.org/10.1007/BF01066106
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DOI: https://doi.org/10.1007/BF01066106