Geodesic
On invariant measures for classical dynamical systems with infinite-dimensional phase space
Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 291-303 
A. A. Arsen'ev. On invariant measures for classical dynamical systems with infinite-dimensional phase space. Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 291-303. http://geodesic.mathdoc.fr/item/SM_1984_49_2_a1/
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     title = {On invariant measures for classical dynamical systems with infinite-dimensional phase space},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Kubo–Martin–Schwinger state is constructed for a Hamiltonian dynamical system whose phase space is Hilbert space, with Hamiltonian representable as the sum of two terms: the square of the norm and a function that is smooth on the completion of the original space in the nuclear norm. Bibliography: 5 titles.

[1] Segal I., “Differential operator in the manifold of rolutions of a non-linear differential equations. I, II”, J. Math. Pure Appl., 44:1–2 (1965), 71–105 | MR

[2] Segal I., “Dispersion for non-linear relativistic equations”, Ann. Sci. Ecole Norm. Super (4), 1:4 (1968), 459–497 | MR | Zbl

[3] Chernoff P. R., Maroden J. E., Properties of Infinite Dimensional Hamiltonian Systems, No 425, Lecture Notes in Math., 1974

[4] Vinogradov A. M., Kupershmidt B. A., “Struktura gamiltonovoi mekhaniki”, UMN, 32:4 (1977), 175–236 | MR | Zbl

[5] Go Kh.-S., Gaussovskie mery v banakhovykh prostranstvakh, Mir, M., 1979