Eigenvalues of Schrödinger operators with complex surface potentials
Abstract
We consider Schrödinger operators in $\mathbb R^d$ with complex potentials supported on a hyperplane and show that all eigenvalues lie in a disk in the complex plane with radius bounded in terms of the $L^p$ norm of the potential with $d-1<p\leq d$. We also prove bounds on sums of powers of eigenvalues.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2015
- DOI:
- 10.48550/arXiv.1512.09067
- arXiv:
- arXiv:1512.09067
- Bibcode:
- 2015arXiv151209067F
- Keywords:
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- Mathematics - Spectral Theory;
- Mathematical Physics
- E-Print:
- 12 pages