Eigenvalue asymptotics for the Schrödinger operators on the real and the complex hyperbolic spaces
type: Item
instance of: scholarly article
title: Eigenvalue asymptotics for the Schrödinger operators on the real and the complex hyperbolic spaces
zbMATH Open document ID: 1072.35136
author: Yuzuru Inahama
author: Shin-Ichi Shirai
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2004-11-23T00:00:00Z
review text: The authors study the spectral asymptotics of large eigenvalues of Schrödinger operators \(-\Delta + V\) on real and complex hyperbolic \(n\)-space \(H^n\) and \(H^n_c\). The non-compactness of these spaces is substituted by a growth condition on the potential \(V\) yielding compactness of the classical phase space and effective compactness of the heat kernel. A Tauberian result turns the control of the heat kernel into an estimate on the counting function which becomes semi-classical for large eigenvalues.
reviewed by: Heinz Siedentop
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 2118460
zbMATH Keywords: spectral asymptotics
zbMATH Keywords: Laplacian
zbMATH Keywords: hyperbolic space
zbMATH Keywords: semiclassical result
MaRDI profile type: Publication
full work available at URL: j.matpur.2004.01.005
OpenAlex ID: W2078468302
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DOI: 10.1016/J.MATPUR.2004.01.005
description: scientific article; zbMATH DE number 2118460