Open AccessExistence of a Bilinear Differential Realization in the Constructions of Tensor Product of Hilbert Spaces
Author(s) -
A. V. Daneev,
Anatoly Lakeyev,
В. А. Русанов
Publication year - 2020
Publication title -
wseas transactions on mathematics
Language(s) - English
Resource type - Journals
eISSN - 2224-2880
pISSN - 1109-2769
DOI - 10.37394/23206.2020.19.9
Subject(s) - mathematics , hilbert space , tensor product , bilinear interpolation , differential operator , mathematical analysis , nonlinear system , pure mathematics , statistics , physics , quantum mechanics
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 RayleighRitz 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.