Singularly continuous spectrum of a self-similar Laplacian on the half-line

被引：11

作者：

Chen, Joe P. ^{[1
]}

Teplyaev, Alexander ^{[1
]}

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2016年 / 57卷 / 05期

关键词：

DIMENSIONAL QUASI-CRYSTALS; JULIA SETS; RESOLVENT KERNEL; PERIODIC JACOBI; FRACTALS; OPERATORS; DYNAMICS; GAPS; RESISTANCE; DIRICHLET;

D O I：

10.1063/1.4949471

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We investigate the spectrum of the self-similar Laplacian, which generates the so-called "pq random walk" on the integer half-line Z(+). Using the method of spectral decimation, we prove that the spectral type of the Laplacian is singularly continuous whenever p not equal 1/2. This serves as a toy model for generating singularly continuous spectrum, which can be generalized to more complicated settings. We hope it will provide more insight into Fibonacci-type and other weakly self-similar models. Published by AIP Publishing.

引用

页数：10