Darning and Gluing of Diffusions

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• 作者：Wolfhard Hansen
• 关键词：Diffusion ; Brownian motion ; Harmonic function ; Harmonic kernel ; Darning ; Gluing ; Stable compact
• 刊名：Potential Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：46
• 期：1
• 页码：167-180
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Potential Theory; Probability Theory and Stochastic Processes; Geometry; Functional Analysis;
• 出版者：Springer Netherlands
• ISSN：1572-929X
• 卷排序：46

文摘

We study darning of compact sets (darning and gluing of finite unions of compact sets), which are not thin at any of their points, in a potential-theoretic framework which may be described, analytically, in terms of harmonic kernels/harmonic functions or, probabilistically, in terms of a diffusion. This is accomplished without leaving our kind of setting so that the procedure can be iterated without any problem. It applies to darning and gluing of compacts in Euclidean spaces (manifolds) of different dimensions, which is of interest pertaining to recent studies on heat kernels.