Abstract:
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.
Key words:system of difference equations, periodic coefficients, system of discrete Lyapunov equations, exponential dichotomy criterion, Riesz projector.
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