To the Geometrical Theory of Differential Realization of Dynamic Processes in a Hilbert Space*

Existence of a Bilinear Delay Differential Realization of Nonlinear Neurodynamic Process in the Constructions of Entropic Rayleigh Ritz Operator

“…Note that Theorem 2 is the development of the Theorem 3 [16], which confirms its methodological importance in the a posterior simulation of complex dynamic systems [26]. One of the applications of this result is the following statement.…”

“…Note 3. The proof of Theorem 1 can be easily modified to formulate an analogue of Theorem 3 [12], expressing in terms of the angular distance in the Hilbert space the conditions for the existence of a bilinear system (1) that implements bundles 2 1 , N N , each of which has its BDR-model, alongside with that, in a mathematical formulation [11], when the simulated operators of the differential system (1) are stationary, i.e.…”

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

“…Moreover, in the system-theoretical analysis of the continuous weakly structured systems, up to a certain moment, the qualitative results of finite-dimensional realization theory are "mechanically" transferred to the infinite-dimensional case without particular complications. This applies to both stationary and non-stationary differential models of the first order (parabolic equations and systems of diffusion type) in uniformly convex Banach spaces [6] and separable Hilbert spaces [7,8].…”

To Existence of a Nonstationary Quasi-Linear Vector Field Realizing the Expansion of a Control Trajectory Bundle in Hilbert Space

“…In this paper we introduce and study (on the qualitative level) the concept of elementary (singleton) expansion of a countable bundle of non-linear dynamic processes allowing differential implementation in the class of quasi-linear controlled systems in the infinite-dimensional Hilbert space. The re-ceived results are a natural evolution of non-linear system analysis of complex differential models [13] and may be useful in the study of inverse problems for partial differential equations [4,5]; statement of the problem considered below, was proposed in the conclusions of the work [3].…”

“…we present a variant of characteristic conditions of equality(3).Theorem If we implement T 0 =  (mod μ) offer is valid: Е   * =  Е   *    L 2 (T, *  ,R) = L 2 (T, * ,R). Proof.…”