The uniqueness of the integrated density of states for the Schrödinger operators for the Robin boundary conditions.
type: Item
instance of: scholarly article
title: The uniqueness of the integrated density of states for the Schrödinger operators for the Robin boundary conditions.
zbMATH Open document ID: 1183.81065
author: Takuya Mine
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2002-11-20T00:00:00Z
review text: Summary: The integrated density of states (IDS) for the Schrödinger operators is defined by using the eigenvalue counting function of the operator restricted to bounded regions with appropriate boundary conditions. Two sufficient conditions for the coincidence of the IDS for the Dirichlet boundary conditions and the IDS for the Robin boundary conditions are given. The proofs of some fundamental formulas, e.g. the change of variables, the chain rule and the divergence formula, for Lipschitz domains are given for the completeness.
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 82B44
zbMATH DE Number: 1833280
zbMATH Keywords: Magnetic Schrödinger operator
zbMATH Keywords: integrated density of states
zbMATH Keywords: Robin boundary conditions
zbMATH Keywords: Lipschitz domain
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1145476342
OpenAlex ID: W1967332551
cites work: Q3756011
cites work: L'asymptotique de Weyl pour les bouteilles magnétiques. (The Weyl asymptotic formula for magnetic bottles)
cites work: The uniqueness of the integrated density of states for the Schrödinger operators with magnetic fields
cites work: The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials
cites work: Uniqueness of the self-adjoint extension of singular elliptic differential operators
cites work: Q5526485
cites work: Schrödinger operators with singular magnetic vector potentials
cites work: A remark on the Dirichlet-Neumann decoupling and the integrated density of states
cites work: Q4340161
cites work: Q3760934
DOI: 10.2977/PRIMS/1145476342
description: scientific article; zbMATH DE number 1833280