具有指数权重的序列空间。Colombeau型代数的实现

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2007-01-01 DOI:10.4064/DM447-0-1

A. Delcroix, M. Hasler, S. Pilipovic, V. Valmorin

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引用次数: 19

摘要

在给定局部凸函数代数的序列空间上引入伪超变换的基础上，给出了各种广义函数代数的描述。我们研究了微局部分析所需要的这些代数的簇性质，并考虑了正则性理论、泛函性以及统一设置下的关联和弱等式的不同概念。利用这种方法，我们还得到了关于超分布和超函数空间嵌入到广义函数的相应代数中的新结果。

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Sequence spaces with exponent weights. Realizations of Colombeau type algebras

We give a description of various algebras of generalized functions based on the introduction of pseudo-ultranorms on spaces of sequences in given locally convex function algebras. We study sheaf properties of these algebras, needed for microlocal analysis, and also consider regularity theory, functoriality and diﬀerent concepts of association and weak equality in a uniﬁed setting. Using this approach, we also give new results on embeddings of ultradistribution and hyperfunction spaces into corresponding algebras of generalized 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.