Distributions in spaces with thick submanifolds

arXiv - MATH - Functional Analysis Pub Date : 2024-08-05 DOI:arxiv-2408.02864

Jiajia Ding, Jasson Vindas, Yunyun Yang

引用次数: 0

Abstract

This article generalizes the results of [J. Math. Anal. Appl. 512 (2022), Article No. 126075], which presented a theory of distributions (generalized functions) with a singular curve contained in the domain of the test functions. In this present article we construct a theory of distributions in $\mathbb{R}^n$ with a ``thick submanifold'', that is, a new theory of thick distributions in $\mathbb{R}^n$ whose domain contains a submanifold on which test functions may be singular.

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具有厚子曲面的空间中的分布

本文概括了[J. Math. Anal. Appl. 512 (2022),文章编号：126075]的结果，该结果提出了一种在检验函数域中包含奇异曲线的分布（广义函数）理论。在本文中，我们构建了一个在$\mathbb{R}^n$中具有 "厚子曲面 "的分布理论，即一个新的在$\mathbb{R}^n$中的厚分布理论，其域包含一个子曲面，在该曲面上测试函数可能是奇异的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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arXiv - MATH - Functional Analysis

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