Header

UZH-Logo

Maintenance Infos

On double eigenvalues of Schrödinger operators on two-dimensional tori


Kappeler, T (1993). On double eigenvalues of Schrödinger operators on two-dimensional tori. Journal of Functional Analysis, 115(1):166-183.

Abstract

An abstract result concerning double eigenvalues of seif-adjoint operators is presented. It is applied to Schrödinger operators -Δ + V on a generic flat torus R2/Γ with V∈C∞(R/Γ): Given N ≥ 1 and ε{lunate} > 0 there exists a potential W in C∞(R2,Γ) such that (i) -Δ + V + W has at least N double eigenvalues and (ii) ||W||L∞ ≤ ε{lunate}. It is also explained why a similar result for Schrödinger operators on S2 is unlikely to hold. © 1993 Academic Press. All rights reserved.

Abstract

An abstract result concerning double eigenvalues of seif-adjoint operators is presented. It is applied to Schrödinger operators -Δ + V on a generic flat torus R2/Γ with V∈C∞(R/Γ): Given N ≥ 1 and ε{lunate} > 0 there exists a potential W in C∞(R2,Γ) such that (i) -Δ + V + W has at least N double eigenvalues and (ii) ||W||L∞ ≤ ε{lunate}. It is also explained why a similar result for Schrödinger operators on S2 is unlikely to hold. © 1993 Academic Press. All rights reserved.

Statistics

Altmetrics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1993
Deposited On:29 Nov 2010 16:29
Last Modified:06 Dec 2017 21:08
Publisher:Elsevier
ISSN:0022-1236
Publisher DOI:https://doi.org/10.1006/jfan.1993.1085
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1228146
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0808.35082

Download

Full text not available from this repository.
View at publisher