Geodesic
On the differential realization of a second-order bilinear system in a Hilbert space
Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 2, pp. 27-36

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We study the necessary and sufficient conditions for the existence of a nonlinear differential realization of a continuous infinite-dimensional behaviorist system in the class of nonstationary second-order bilinear ordinary differential (in particular, hyperbolic) equations in a separable Hilbert space. The obtained conditions rely upon the tensor products of Hilbert spaces. In passing, we analytically justify some topological-metrical continuity conditions for the projectivization of the Rayleigh–Ritz operator with the calculation of the fundamental group of its image.
Keywords: inverse problem of nonlinear system analysis, bilinear differential realization. 
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     author = {A. V. Lakeyev and Yu. E. Linke and V. A. Rusanov},
     title = {On the differential realization of a second-order bilinear system in a {Hilbert} space},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {27--36},
     publisher = {mathdoc},
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     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2019_22_2_a2/}
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A. V. Lakeyev; Yu. E. Linke; V. A. Rusanov. On the differential realization of a second-order bilinear system in a Hilbert space. Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 2, pp. 27-36. http://geodesic.mathdoc.fr/item/SJIM_2019_22_2_a2/