The theory of thick distributions (both in dimension 1 and in higher dimensions) was constructed in recent years [7, 27]. However this theory of distributions with one thick point in dimension one is very different from that in higher dimensions. In this paper the author uses the language of asymptotic analysis to reconstruct the 1-dimensional thick distribution theory and to incorporate it into the framework of the higher-dimensional thick distribution theory. Some new concepts and interesting results appear in this paper from viewing singular functions in a different way.

中文翻译：

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一维厚分布理论的重构

厚分布理论（在维度 1 和更高维度）是近年来构建的 [7, 27]。然而，这种在第一维有一个粗点的分布理论与更高维的分布理论有很大不同。在本文中，作者使用渐近分析语言重构一维厚分布理论，并将其纳入高维厚分布理论的框架中。一些新的概念和有趣的结果出现在本文中，从不同的角度来看奇异函数。