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-valued 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
pβ[1,β). The sharpness of the results are demonstrated by means of
explicit examples.Comment: References added before Theorem 2 and