TY - JOUR

T1 - Properties of Solutions to Systems of Difference Equations with Periodic Coefficients

AU - Demidenko, G. V.

AU - Bondar, A. A.

AU - Ganzhaeva, M. Sh.

N1 - Demidenko, G.V., Bondar, A.A. & Ganzhaeva, M.S. Properties of Solutions to Systems of Difference Equations with Periodic Coefficients. Sib. Adv. Math. 35, 287–304 (2025). https://doi.org/10.1134/S1055134425040029 The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0008).

PY - 2025/12/22

Y1 - 2025/12/22

N2 - In the present article, we consider systems of linear difference equations with periodic coefficients such that the spectrum of the monodromy matrix and the unit circle are disjoint. We find bounded solutions to such systems. For these solutions, we prove uniqueness theorems, obtain formulas, and estimate the norm. In certain partial cases, the estimates coincide with Kreĭn’s inequalities.

AB - In the present article, we consider systems of linear difference equations with periodic coefficients such that the spectrum of the monodromy matrix and the unit circle are disjoint. We find bounded solutions to such systems. For these solutions, we prove uniqueness theorems, obtain formulas, and estimate the norm. In certain partial cases, the estimates coincide with Kreĭn’s inequalities.

KW - system of difference equations

KW - periodic coefficients

KW - system of discrete Lyapunov equations

KW - exponential dichotomy criterion

KW - Riesz projector

UR - https://www.scopus.com/pages/publications/105025413883

M3 - Article

VL - 35

SP - 287

EP - 304

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 4

ER -