拟解析泛函和作为调和函数边值的超分布

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-10 DOI:10.4171/prims/59-3-8

Andreas Debrouwere, Jasson Vindas

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引用次数: 2

摘要

研究了拟解析泛函空间和非拟解析型超分布空间中调和函数的边值。作为一个应用，我们提供了一种新的方法来研究Hörmander的准解析泛函的支持定理。我们的主要技术工具是用几乎调和函数来描述超可微函数，这是我们在本文中引入的一个概念。我们在由权矩阵定义的超可微类的集合中工作。特别是，我们的结果同时适用于通过权重序列和权重函数定义的两个标准类。

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Quasianalytic Functionals and Ultradistributions as Boundary Values of Harmonic Functions

We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a new approach to Hörmander’s support theorem for quasianalytic functionals. Our main technical tool is a description of ultradifferentiable functions by almost harmonic functions, a concept that we introduce in this article. We work in the setting of ultradifferentiable classes defined via weight matrices. In particular, our results simultaneously apply to the two standard classes defined via weight sequences and via weight functions.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.