论文标题
Neumann-Poincaré操作员的光谱分析
Spectral analysis of Neumann-Poincaré operator
论文作者
论文摘要
这是对一个多世纪的累积光谱分析观测值的调查，指的是双层潜在积分方程，也称为Neumann-Poincaré运算符。光谱分析的概念沿着这条路径发展。的确，最初旨在阐明经典潜在理论问题的特定奇异积分方程的寻求启发并塑造了XX至1世纪线性变换的理论光谱分析的发展。我们简要介绍了该主题的一些标记发现，并充分说明了旧的，有时被遗忘的文字和新贡献的书目参考。值得注意的是，如今仍未发现Neumann-Poincaré操作员的光谱分析的应用，对应用科学产生了壮观的影响。在我们的调查中描述了沿着这些线的一些现代影响。
This is a survey of accumulated spectral analysis observations spanning more than a century, referring to the double layer potential integral equation, also known as Neumann-Poincaré operator. The very notion of spectral analysis has evolved along this path. Indeed, the quest for solving this specific singular integral equation, originally aimed at elucidating classical potential theory problems, has inspired and shaped the development of theoretical spectral analysis of linear transforms in XX-th century. We briefly touch some marking discoveries into the subject, with ample bibliographical references to both old, sometimes forgotten, texts and new contributions. It is remarkable that applications of the spectral analysis of the Neumann-Poincaré operator are still uncovered nowadays, with spectacular impacts on applied science. A few modern ramifications along these lines are depicted in our survey.
