Interconnected systems for the Lyapunov’s linear operator equations in the Hilbert space - Oleksandr Pokutnyi; Yevhen Panasenko; Olena Polishchuk (Franklin Open, 2025)
This paper investigates a perturbed interconnected system for linear operator Lyapunov equations in Hilbert space. We establish solvability conditions for the operator system in cases where the generating system of equations does and does not have solutions. Solutions are sought in the form of a completely convergent series.