Sharp spectral bounds for complex perturbations of the indefinite Laplacian |
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Authors: | Jean-Claude Cuenin Orif O. Ibrogimov |
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Affiliation: | 1. Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom;2. Institute for Theoretical Physics, ETH Zürich, Wolfgang-Pauli-Str. 27, 8093 Zürich, Switzerland |
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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 -potentials, we obtain optimal spectral enclosures which accommodate also embedded eigenvalues, while our result for -potentials yield sharp spectral bounds on the imaginary parts of eigenvalues of the perturbed operator for all . The sharpness of the results are demonstrated by means of explicit examples. |
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Keywords: | Indefinite Laplacian Spectrum (Embedded) eigenvalue Lieb-Thirring inequality |
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