Discrete Schäffer spaces and exponential dichotomy for evolution families

Preda, Ciprian; Onofrei, Oana Romina

doi:10.1007/s00605-016-0991-0

Cited by 4 publications

(2 citation statements)

References 14 publications

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“…The dichotomy of various abstract difference equations has been investigated by many mathematicians, cf. [4] and [5][6][7][8][9][10][11] and the references therein. In particular, the main result of the paper [8] gives a decomposition of the dichotomy spectrum considering the upper dichotomy spectrum, lower dichotomy spectrum, and essential dichotomy spectrum.…”

Section: Introduction and Notationsmentioning

confidence: 99%

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

Gil’

2019

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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.

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Section: Introduction and Notationsmentioning

confidence: 99%

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

Gil’

2019

Axioms

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“…For more recent results devoted to continuous and discrete evolution families, we refer to [5][6][7][8][9][10][11][12][13][14][15] for those dealing with uniform exponential behaviour and to [16][17][18][19][20] for those that consider various concepts of nonuniform exponential behaviour.…”

Section: Introductionmentioning

confidence: 99%