Next Article in Journal
3-Lie Superalgebras Induced by Lie Superalgebras
Next Article in Special Issue
Heteroclinic Solutions for Classical and Singular ϕ-Laplacian Non-Autonomous Differential Equations
Previous Article in Journal / Special Issue
Note on Limit-Periodic Solutions of the Difference Equation xt + 1 − [h(xt) + λ]xt = rt, λ > 1
Open AccessArticle

Solution Estimates for the Discrete Lyapunov Equation in a Hilbert Space and Applications to Difference Equations

Department of Mathematics, Ben Gurion University of the Negev, P.0. Box 653, Beer-Sheva 84105, Israel
Axioms 2019, 8(1), 20; https://doi.org/10.3390/axioms8010020
Received: 15 January 2019 / Revised: 1 February 2019 / Accepted: 2 February 2019 / Published: 6 February 2019
(This article belongs to the Special Issue New Trends in Differential and Difference Equations and Applications)
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-Text
Keywords: discrete Lyapunov equation; difference equations; Hilbert space; dichotomy; exponential stability discrete Lyapunov equation; difference equations; Hilbert space; dichotomy; exponential stability
MDPI and ACS Style

Gil’, M. Solution Estimates for the Discrete Lyapunov Equation in a Hilbert Space and Applications to Difference Equations. Axioms 2019, 8, 20.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop