Existence of a Bilinear Differential Realization in the Constructions of Tensor Product of Hilbert Spaces

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Abstract: The paper describes the results of a functional-geometric study of the necessary and sufficient conditions for the existence of a differential realization in the terms of the tensor product of real Hilbert spaces. There are considered continuous infinite-dimensional dynamical system in the class of controlled bilinear nonstationary ordinary differential equations of the second order (including quasi-linear hyperbolic models) in a separable Hilbert space. Therefore the topological and metric conditions for the continuity of the RayleighRitz operator with the calculation of the fundamental group of its image are analytically substantiated. The results of paper give incentives for generalizations in the qualitative theory of nonlinear structural identification of higher order multi-linear differential models.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 19, 2020, Art. #9

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Aleksey Daneev, Aleksey Daneev, Anatoliy Lakeyev, "Existence of a Bilinear Differential Realization in the Constructions of Tensor Product of Hilbert Spaces," WSEAS Transactions on Mathematics, vol. 19, pp. 99-107, 2020, DOI:10.37394/23206.2020.19.9
Aleksey Daneev, Aleksey Daneev, Anatoliy Lakeyev. Existence of a Bilinear Differential Realization in the Constructions of Tensor Product of Hilbert Spaces. WSEAS Transactions on Mathematics. 2020;19:99-107. 10.37394/23206.2020.19.9
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