发表机构
School of Mathematics and Statistics, Lanzhou University（兰州大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究相容调和测度系统的同步边界与核逼近，通过联合极限、有限分解及粘合映射，在极小边界上建立唯一表示测度，并用经典调和函数等例子阐明结论差异。
AI 中文摘要
我们研究相容调和测度系统的同步边界与核逼近。内边界测度与核的联合极限在边界上给出一个同时保留位置与核信息的表示。有限分解给出在极小核上的集中性，核集中性给出函数投影的唯一性。沿一条公共子序列的边界集中性在给定的紧致细化上实现该表示。随后一个粘合映射在极小边界上给出唯一的表示测度。一个邻域非消失条件给出沿全序列的同步选择。经典调和函数、带分裂边界点的圆盘以及有限加权度量图说明了这些结论之间的区别。
英文摘要
We study synchronized boundary and kernel approximation for harmonic measure systems satisfying nested mean-value identities. Under boundary concentration along a common subsequence, joint limits yield representation on a common refinement, and gluing gives uniqueness on the minimal boundary. Neighborhood nonvanishing gives full-sequence synchronized selection. For a compact set whose removal from a bounded $C^{1,1}$ domain in dimension at least three leaves a connected domain, zero Newtonian capacity is equivalent to concentration of one normalized singular kernel, constructed from harmonic measures, on a subsequence of one relatively compact exhaustion. For such zero-capacity sets, capacitary estimates give quantitative recovery of finite signed source measures on every prescribed relatively compact exhaustion. On rectifiable curve networks in three dimensions, the logarithmic error bound is sharp for this recovery formula in the class of finite measures. Boundary splitting and finite weighted metric graphs illustrate the gluing conclusions.
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