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Sharp spectral bounds for complex perturbations of the indefinite Laplacian

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journal contribution
posted on 12.11.2020, 10:19 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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Functional Analysis

Volume

280

Issue

1

Publisher

Elsevier

Version

AM (Accepted Manuscript)

Rights holder

© Elsevier

Publisher statement

This 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

Acceptance date

23/09/2020

Publication date

2020-09-28

Copyright date

2020

ISSN

0022-1236

eISSN

1096-0783

Language

en

Depositor

Dr Jean-Claude Cuenin. Deposit date: 11 November 2020

Article number

108804

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