Naslov
Admissibility and Polynomial Dichotomy of Discrete Nonautonomous Systems

Autori
Dragičević, Davor ; Sasu, Adina Luminita ; Sasu, Bogdan

Izvornik
Carpathian journal of mathematics (1584-2851) 38 (2022), 3; 737-762

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
ordinary dichotomy ; exponential dichotomy ; polynomial dichotomy ; discrete nonautonomous system ; input-output system ; admissibility ; robustness

Sažetak
We give new admissibility criteria for dichotomic behaviours of discrete nonautonomous systems, in infinite dimensional spaces. In the first part of the paper, we present admissibility conditions for uniform and exponential dichotomy. Next, our study is focused on polynomial dichotomy, providing new characterizations for this notion by means of some double admissibilities. We obtain two categories of criteria for polynomial dichotomy, based on input-output conditions imposed to some suitable systems such that, for each one, the input sequences belong to certain $\ell^p$ -spaces and the outputs are bounded. We point out the importance of the assumptions regarding the complementarity of the stable subspaces at the initial time and we also discuss the relevance of the concept of solvability (unique or not) in the admissibility criteria for polynomial dichotomies on the half-line. All the results are obtained in the general case, without any additional hypotheses on the systems coefficients and without assuming any growth type properties for the associated propagators. Furthermore, as an application of the admissibility results we establish a robustness property of the polynomial dichotomy under small perturbations.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Napomena
Part of the special issue dedicated to the 75th
anniversary of Professor Mihail Megan

POVEZANOST RADA