Foundations of the modified Poisson kernel method were laid out by Finkelstein and Scheinberg in 1975 in the context of explicit solvability for the adaptive Dirichlet problem in a half plane. Over the past decade, this method has been further developed, and new applications have appeared both in the field of harmonic analysis and operator theory and in practical Schrödinger problems. In this paper, we pay special attention to cylindrical Poisson kernel method’s application for the integral representations of harmonic functions in a cylinder.

中文翻译：

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圆柱泊松核方法及其应用

Finkelstein 和 Scheinberg 于 1975 年在半平面中自适应狄利克雷问题的显式可解性背景下奠定了修正泊松核方法的基础。在过去的十年中，这种方法得到了进一步的发展，在谐波分析和算子理论领域以及实际的薛定谔问题中都出现了新的应用。在本文中，我们特别关注圆柱泊松核方法在圆柱内调和函数的积分表示中的应用。