Spectral decimation for families of self-similar symmetric Laplacians on the Sierpiński gasket

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2017-09-07 DOI:10.4171/jfg/83

S. Fang, Dylan A. King, E. Lee, R. Strichartz

引用次数: 4

Abstract

We construct a one-parameter family of Laplacians on the Sierpinski Gasket that are symmetric and self-similar for the 9-map iterated function system obtained by iterating the standard 3-map iterated function system. Our main result is the fact that all these Laplacians satisfy a version of spectral decimation that builds a precise catalog of eigenvalues and eigenfunctions for any choice of the parameter. We give a number of applications of this spectral decimation. We also prove analogous results for fractal Laplacians on the unit Interval, and this yields an analogue of the classical Sturm-Liouville theory for the eigenfunctions of these one-dimensional Laplacians.

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Sierpiński垫片上自相似对称拉普拉斯族的谱抽取

对于由标准3映射迭代函数系统迭代得到的9映射迭代函数系统，我们在Sierpinski垫片上构造了对称自相似的单参数拉普拉斯算子族。我们的主要结果是，所有这些拉普拉斯算子都满足谱抽取的一个版本，它为任何参数的选择建立了一个特征值和特征函数的精确目录。我们给出了这种谱抽取的一些应用。我们还证明了单位区间上分形拉普拉斯算子的类似结果，这就得到了一维拉普拉斯算子本征函数的经典Sturm-Liouville理论的类似结果。

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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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.