Solution Estimates for the Discrete Lyapunov Equation in a Hilbert Space and Applications to Difference Equations
Keyword(s):
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.
2003 ◽
Vol 2003
(48)
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pp. 3059-3066
2008 ◽
Vol 144
(4)
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pp. 867-919
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Keyword(s):
2015 ◽
Vol 15
(3)
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pp. 373-389
2018 ◽
Vol 2018
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pp. 1-13
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