Abstract
We establish different estimates for the sums of negative eigenvalues of elliptic operators. Our proofs are based on a property of the eigenvalue sums that might be viewed as a certain convexity with respect to the perturbation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Birman, M.S.: Perturbations of quadratic forms and the spectrum of singular boundary value problems. Dokl. Akad. Nauk SSSR 125, 471–474 (1959, in Russian)
Birman M.Sh.: Discrete spectrum in the gaps of a continuous one for perturbations with large coupling constants. Adv. Soviet Math. 7, 57–73 (1991)
Hundertmark D., Lieb E., Thomas L.: A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator. Adv. Theor. Math. Phys. 2, 719–731 (1998)
Laptev A., Weidl T.: Sharp Lieb-Thirring inequalities in high dimensions. Acta Math. 184(1), 87–111 (2000)
Open Access
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by A. Laptev.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Molchanov, S., Safronov, O. Negative spectra of elliptic operators. Bull. Math. Sci. 2, 321–329 (2012). https://doi.org/10.1007/s13373-012-0025-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13373-012-0025-8