Pure point spectrum of the Laplacians on fractal graphs
type: Item
instance of: scholarly article
title: Pure point spectrum of the Laplacians on fractal graphs
zbMATH Open document ID: 0822.05045
author: Alexander Teplyaev
author: Leonid Malozemov
published in: Journal of Functional Analysis
publication date: 1995-06-14T00:00:00Z
review text: On two-point self-similar fractal graphs the authors consider Laplacians which correspond to the adjacency matrix and the simple random walk. Roughly speaking, it is proven that if the graph has an infinite number of cycles and the length of these cycles approaches infinity, then the spectrum is pure point and all eigenvalues have infinite multiplicity. It is also shown that a countable set of orthonormal eigenfunctions with compact support is complete.
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 47B80
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 60H25
zbMATH DE Number: 764032
zbMATH Keywords: fractal graphs
zbMATH Keywords: Laplacians
zbMATH Keywords: cycles
zbMATH Keywords: spectrum
zbMATH Keywords: eigenvalues
zbMATH Keywords: orthonormal eigenfunctions
reviewed by: Georgi E. Karadzhov
MaRDI profile type: Publication
full work available at URL: jfan.1995.1056
OpenAlex ID: W2063406007
DOI: 10.1006/JFAN.1995.1056
description: scientific article; zbMATH DE number 764032