On uniform exponential N-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

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...

Exponential Dichotomy for Evolution Families on the Real Line

We give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair (Lp(R,X),Lq(R,X)). We show that the admissibility of the pair (Lp(R,X),Lq(R,X)) is equivalent to the uniform exponential dichotomy of an evolution family if and only if p ≥ q. As applications we obtain characterizations for uniform exponential dichotomy o...