EIGENVALUES OF LAPLACIANS ON HIGHER DIMENSIONAL VICSEK SET GRAPHS

被引：0

作者：

Cao, Shiping ^{[1
]}

Strichartz, Robert S. ^{[1
]}

Wei, Melissa ^{[1
]}

机构：

[1] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2022年 / 30卷 / 01期

关键词：

Vicsek Set; Eigenvalues; Isomorphism of Lattices; SPECTRAL-ANALYSIS; SIERPINSKI; EIGENFUNCTIONS; FRACTALS; GAPS;

D O I：

10.1142/S0218348X22500190

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the graphs associated with Vicsek sets in higher dimensional settings. First, we study the eigenvalues of the Laplacians on the approximating graphs of the Vicsek sets, finding a general spectral decimation function. This is an extension of earlier results on two-dimensional Vicsek sets. Second, we study the Vicsek set lattices, which are natural analogues to the Sierpinski lattices. We have a criterion when two different Vicsek set lattices are isomorphic.

引用

页数：13

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[3]

[Anonymous], 1998, Diffusion on Fractals, DOI DOI 10.1007/BFB0092537

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