Spectral estimates for Schrödinger and Dirac-type operators on Riemannian manifolds
type: Item
instance of: scholarly article
title: Spectral estimates for Schrödinger and Dirac-type operators on Riemannian manifolds
zbMATH Open document ID: 0791.58094
DOI: 10.1007/BF01459757
author: Manlio Bordoni
published in: Mathematische Annalen
publication date: 1994-05-05T00:00:00Z
full work available at URL: https://eudml.org/doc/165192
review text: From a Hilbertian theorem (which generalizes a Theorem of S. Gallot and D. Meyer), we deduce a general criterion to compare the spectra of two operators \(T\) and \(T'\) acting on Hilbert spaces \(H\) and \(H'\), under the assumption that they verify Kato's inequality with respect to a map \(\omega: H' \to H\). We apply this principle in several contexts. We obtain estimates for the spectra of Schrödinger and Dirac-type operators by the spectrum of the Riemannian base manifold. Our results contain, as particular cases, previous estimates given by other authors (S. Gallot and D. Meyer for the Hodge-de Rham Laplacian acting on differential forms, T. Friedrich for Dirac operator acting on spinors). The criterion, applied to Riemannian submersions, or coverings, or local quasi-isometries, gives estimates of the spectrum of the total space in terms of the spectrum of the base manifold.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C27
zbMATH DE Number: 562483
zbMATH Keywords: comparison of spectra
zbMATH Keywords: Schrödinger
zbMATH Keywords: Hodge-de Rham
zbMATH Keywords: Dirac operator
zbMATH Keywords: Riemannian submersions
zbMATH Keywords: coverings
zbMATH Keywords: local quasi-isometries
Wikidata QID: Q115393423
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 562483