Spectral decimation for a graph-directed fractal pair  

作　　者：Shiping Cao Hua Qiu Haoran Tian Lijian Yang 

机构地区：[1]Department of Mathematics,Cornell University,Ithaca,NY14850,USA [2]Department of Mathematics,Nanjing University,Nanjing 210093,China [3]Department of Mathematics,University of Kansas,KS 66045,USA

出　　处：《Science China Mathematics》2022年第12期2503-2520,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.12071213);the Natural Science Foundation of Jiangsu Province in China(Grant No.BK20211142);。

摘　　要：We introduce a graph-directed pair of planar self-similar sets that possess fully symmetric Laplacians. For these two fractals, due to Shima’s celebrated criterion, we point out that one admits the spectral decimation by the canonic graph approximation and the other does not. For the second fractal, we adjust to choosing a new graph approximation guided by the directed graph, which still admits spectral decimation. Then we make a full description of the Dirichlet and Neumann eigenvalues and eigenfunctions of both of these two fractals.

关 键 词：fractal Laplacian spectral decimation Dirichlet spectrum Neumann spectrum 

分 类 号：O157.5[理学—数学]