Exact bounds for exponential dichotomy roughness III. Semistrong 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.

Exact Dichotomy-based Constrained Encoding

Constrained encoding has several applications in the synthesis of finite state machines (FSMs). E.g., it can be used to generate asynchronous FSM state assignment that guarantees a critical hazard-free implementation, or to generate synchronous FSM state assignment with minimum PLA implementation. This paper presents ZEDICHO, an original zero-suppressed binary decision diagram (ZBDD) based algo...

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.

On Exponential Dichotomy of Variational Difference Equations

Discrete Methods and Exponential Dichotomy of Semigroups

The aim of this paper is to characterize the uniform exponential dichotomy of semigroups of linear operators in terms of the solvability of discrete-time equations over N. We give necessary and sufficient conditions for uniform exponential dichotomy of a semigroup on a Banach space X in terms of the admissibility of the pair (l∞(N, X), c00(N, X)). As an application we deduce that a C0-semigroup...