Sharp spectral bounds for complex perturbations of the indefinite Laplacian

Abstract

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. © 2020 Elsevier Inc.