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

Abstract

In the context of the qualitative theory of realization of infinite-dimensional dynamic systems, the authors demonstrate some results related to investigation of the geometrical properties of families of continuous controlled dynamic processes (“input–output” mappings) in the problem of solvability of this differential realization in a class of linear ordinary non-stationary differential equations in a separable Hilbert space.