In the half-plane, the Dirichlet problem is considered for elliptic differential-difference equations with nonlocal general-kind potentials, which are linear combinations of translations of the desired function, not bounded by commensurability conditions. We find a condition for the symbol of the corresponding differential-difference operator, providing the classical solvability of the specified problem for each continuous and bounded boundary-value function. The representation of the specified classical solution by a Poisson-type integral is constructed.

中文翻译：

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具有一般类非局部势的半平面微分椭圆问题

在半平面中，Dirichlet 问题被考虑用于具有非局部一般类势的椭圆微分方程，它们是所需函数的平移的线性组合，不受可公度条件的限制。我们为相应的微分差分算子的符号找到了一个条件，为每个连续和有界的边界值函数提供了指定问题的经典可解性。构造了用泊松型积分表示的指定经典解。