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On the Differential Realization of a Second-Order Bilinear System in a Hilbert Space

Авторы: Lakeyev A.V., Linke Y.E., Rusanov V.

Журнал: Journal of Applied and Industrial Mathematics

Том: 13

Номер: 2

Год: 2019

Отчётный год: 2019

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Аннотация: 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.

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