Cluster expansion of the resolvent for the Schrödinger operator on non-percolating graphs with applications to Simon-Spencer type theorems and localization
type: Item
instance of: scholarly article
title: Cluster expansion of the resolvent for the Schrödinger operator on non-percolating graphs with applications to Simon-Spencer type theorems and localization
zbMATH Open document ID: 1377.31004
DOI: 10.4171/JST/176
author: Lukun Zheng
author: S. Molchanov
published in: Journal of Spectral Theory
publication date: 2017-11-01T00:00:00Z
review text: Summary: The paper contains a generalization of the well-known 1D results on the absence of the a.c. spectrum (in the spirit of the Simon-Spencer theorem) and localization to the wide class of ``non-percolating'' graphs, which include the Sierpiński lattice and quasi 1D trees. The main tools are cluster expansion of the resolvent and real analytic techniques (Kolmogorov's lemma and similar estimates).
Mathematics Subject Classification ID: 31C20
Mathematics Subject Classification ID: 35R02
zbMATH DE Number: 6801916
zbMATH Keywords: graphs
zbMATH Keywords: lattice Laplacian
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: spectrum
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/jst/176
OpenAlex ID: W2758230446
description: scientific article; zbMATH DE number 6801916