%0 Journal Article
%T Solution Estimates for the Discrete Lyapunov Equation in a Hilbert Space and Applications to Difference Equations
%A Michael Gil¡¯
%J -
%D 2019
%R https://doi.org/10.3390/axioms8010020
%X Abstract The paper is devoted to the discrete Lyapunov equation X £¿ A * X A = C , where A and C are given operators in a Hilbert space H and X should be found. We derive norm estimates for solutions of that equation in the case of unstable operator A, as well as refine the previously-published estimates for the equation with a stable operator. By the point estimates, we establish explicit conditions, under which a linear nonautonomous difference equation in H is dichotomic. In addition, we suggest a stability test for a class of nonlinear nonautonomous difference equations in H . Our results are based on the norm estimates for powers and resolvents of non-self-adjoint operators. View Full-Tex
%K discrete Lyapunov equation
%K difference equations
%K Hilbert space
%K dichotomy
%K exponential stability
%U https://www.mdpi.com/2075-1680/8/1/20