Kappeler, T (1993). On double eigenvalues of Schrödinger operators on two-dimensional tori. Journal of Functional Analysis, 115(1):166-183.
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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Analysis |
| Language: | English |
| Date: | 1993 |
| Deposited On: | 29 Nov 2010 16:29 |
| Last Modified: | 23 Jan 2022 14:47 |
| Publisher: | Elsevier |
| ISSN: | 0022-1236 |
| OA Status: | Closed |
| 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 |
Kappeler, T