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Difference equations, including linear and nonlinear equations, discrete version of topics in analysis, partial difference equations, oscillation theory, periodic solutions, almost periodic solutions, bifurcation theory, stability theory.

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A problem from linear algebra and difference equations

Let $A$ be a linear second-order difference operator acting on the space of complex sequences as $$(Af)_{n}=f_{n-1}+a_{n}f_{n}+f_{n+1}, \quad n\in\mathbb{Z},$$ where $a_{n}\in\mathbb{C}$. Further, let …