On Roughness of Exponential Dichotomy

On Exponential Dichotomy of Semigroups

The aim of this paper is to analyze the connections between the exponential dichotomy of a semigroup on a Banach space X and the admissibility of the pair (`p(N, X), `q(N, X)). We obtain necessary and sufficient conditions for exponential dichotomy of exponentially bounded semigroups using discrete time techniques.

On Exponential Dichotomy of Variational Difference Equations

Roughness of (ℤ+, ℤ−)-Nonuniform Exponential Dichotomy for Difference Equations in Banach Spaces

In this paper we study the roughness of (ℤ+, ℤ-)-nonuniform exponential dichotomy for nonautonomous difference equations in the general context of infinite-dimensional spaces. An explicit form is given for each of the dichotomy constants of the perturbed equation in terms of the original ones. We emphasize that we do not assume any boundedness condition on the coefficients.

Exponential Stability, Exponential Expansiveness, and Exponential Dichotomy of Evolution Equations on the Half-line

For an evolution family on the half-line U = (U(t; s)) ts0 of bounded linear operators on a Banach space X we introduce operators G 0 ; G X and I X on certain spaces of X-valued continuous functions connected with the integral equation u(t) = U(t; s)u(s) + R t s U(t;)f()dd: We characterize exponential stability, exponential expansiveness and exponential dichotomy of U by properties of G 0 ; G X...

Exponential Stability and Exponential Dichotomy of Semigroups of Linear Operators

The aim of this paper is to establish necessary and sufficient conditions for exponential stability of semigroups of linear operators and to show how this conditions can be applied in order to characterize the exponential dichotomy. First, we prove that an exponentially bounded semigroup is exponentially stable if and only if it is (l(N, X), l∞(N, X))-stable, where p ∈ (1,∞). After that this re...