Exact Hausdorff dimension of the spectral measure for the graph Laplacian on a sparse tree

被引：0

作者：

Ujino, Kota ^{[1
]}

机构：

[1] Kyushu Univ, Grad Sch Math, Nishi Ku, 744 Motooka, Fukuoka 8190395, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 519卷 / 02期

关键词：

Graph Laplacian; Singular continuous spectrum; Sparse potential; Hausdorff dimension; Intermittency function; SINGULAR CONTINUOUS-SPECTRUM; SUBORDINACY; OPERATORS;

D O I：

10.1016/j.jmaa.2022.126811

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Hausdorff dimension of spectral measure for the graph Laplacian is shown exactly in terms of an intermittency function. The intermittency function can be estimated by using one-dimensional discrete Schrodinger operator method. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：39

共 15 条

[1] A Mourre estimate for a Schrodinger operator on a binary tree
Allard, C
Froese, N
[J]. REVIEWS IN MATHEMATICAL PHYSICS, 2000, 12 (12) : 1655 - 1667
[2] Remarks on the relation between quantum dynamics and fractal spectra
Barbaroux, JM
Combes, JM
Montcho, R
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 213 (02) : 698 - 722
[3] Singular continuous spectrum for the Laplacian on certain sparse trees
Breuer, Jonathan
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2007, 269 (03) : 851 - 857
[4] On the Decomposition of the Laplacian on Metric Graphs
Breuer, Jonathan
Levi, Netanel
[J]. ANNALES HENRI POINCARE, 2020, 21 (02): : 499 - 537
[5] Davies E., 1995, SPECTRAL THEORY DIFF
[6] DiBenedetto E., 2002, REAL ANAL
[7] Falconer K.J., 1997, TECHNIQUES FRACTAL G, V3
[8] ON SUBORDINACY AND ANALYSIS OF THE SPECTRUM OF ONE-DIMENSIONAL SCHRODINGER-OPERATORS
GILBERT, DJ
PEARSON, DB
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1987, 128 (01) : 30 - 56
[9] Power-law subordinacy and singular spectra I. Half-line operators
Jitomirskaya, S
Last, Y
[J]. ACTA MATHEMATICA, 1999, 183 (02) : 171 - 189
[10] Essential self-adjointness of the graph-Laplacian
Jorgensen, Palle E. T.
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (07)

← 1 2 →