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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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Solutions of complex linear difference equations

I'm wondering what the solutions of complex linear difference equations like \begin{equation} f(z+\eta_1)+f(z+\eta_2)+\ldots+f(z+\eta_n)=0,\ \ \ \eta_1 \cdots\eta_n \in \mathbf{C} \end{equation} look …