6. Papers

Properties of solutions to systems of difference equations with periodic coefficients

Gennadii V. Demidenko
Scopus Author ID: 6701652666
1. Sobolev Institute of Mathematics SBRAS, Novosibirsk, Russia
2. Novosibirsk State University, Novosibirsk, Russia
demidenk@math.nsc.ru
Anna A. Bondar
Scopus Author ID: 57192653521
1. Novosibirsk State University, Novosibirsk, Russia
anna.alex.bondar@gmail.com
Mardona Sh. Ganzhaeva
1. Novosibirsk State University, Novosibirsk, Russia
m.ganzhaeva@g.nsu.ru
The material was received by the Editorial Board: 10.06.2025

The paper is devoted to finding bounded solutions to systems of linear difference equations with periodic coefficients,provided that the spectrum of the monodromy matrix does not intersect with the unit circle.Theorems on unique solvability are proved, solution formulas are obtained, and estimates of the solution norm are established.In particular cases, these estimates coincide with Krein's inequalities.

УДК 517.962.22

Properties of solutions to systems of difference equations with periodic coefficients
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Keywords: system of difference equations, periodic coefficients, system of discrete Lyapunov equations, exponential dichotomy criterion, Riesz projector.


References: Gennadii V. Demidenko, Anna A. Bondar, Mardona Sh. Ganzhaeva Properties of solutions to systems of difference equations with periodic coefficients. Mat. Trudy. 2025, 28, №3. P. 19–49. DOI: 10.25205/1560-750X-2025-28-3-19-49