基于$n$-立方体的自相似集上的组合Fredholm模

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2019-12-12 DOI:10.4171/jfg/132

T. Maruyama, Tatsuki Seto

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引用次数: 1

摘要

我们在自相似集(如康托尘、谢尔宾斯基地毯和门格尔海绵)上构造了一个Fredholm模块。我们的构造是Connes在康托集上的Fredholm模块的组合构造的高维模拟。我们还计算了由Fredholm模引起的两个算子的Dixmier迹。

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A combinatorial Fredholm module on self-similar sets built on $n$-cubes

We construct a Fredholm module on self-similar sets such as the Cantor dust, the Sierpinski carpet and the Menger sponge. Our construction is a higher dimensional analogue of Connes' combinatorial construction of the Fredholm module on the Cantor set. We also calculate the Dixmier trace of two operators induced by the Fredholm module.

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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.

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