Exponential dichotomy and (ℓp,ℓq)-admissibility on the half-line

By Bogdan Sasu, Adina Luminita Sasu. 2006

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Abstract We give necessary and sufficient conditions for uniform exponential dichotomy of discrete evolution families in terms of the admissibility of the pair ( l p ( N , X ) , l 0 q ( N , X ) ) . We prove that the admissibility of the pair ( l p ( N , X ) , l 0 q ( N , X ) ) is a sufficient condition for uniform exponential dichotomy of a discrete evolution family. This condition becomes necessary for discrete evolution families with uniform exponential growth if and only if p ⩾ q . As consequences, we obtain necessary and sufficient conditions for uniform exponential dichotomy of evolution families.

Subfields: Applied Mathematics, Control and Systems Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/432f7b74aa693861154c4c617d54dec5de58d014