Sharp spectral bounds for complex perturbations of the indefinite Laplacian
journal contributionposted on 2020-11-12, 10:19 authored by Jean-Claude CueninJean-Claude Cuenin, OO Ibrogimov
© 2020 Elsevier Inc. We derive quantitative bounds for eigenvalues of complex perturbations of the indefinite Laplacian on the real line. Our results substantially improve existing results even for real potentials. For L1-potentials, we obtain optimal spectral enclosures which accommodate also embedded eigenvalues, while our result for Lp-potentials yield sharp spectral bounds on the imaginary parts of eigenvalues of the perturbed operator for all p∈[1,∞). The sharpness of the results are demonstrated by means of explicit examples.
- Mathematical Sciences
Published inJournal of Functional Analysis
- AM (Accepted Manuscript)
Rights holder© Elsevier
Publisher statementThis paper was accepted for publication in the journal Journal of Functional Analysis and the definitive published version is available at https://doi.org/10.1016/j.jfa.2020.108804