BooksecrCollected Volumepp. 245–259

Eigenvalues of Schrödinger operators with complex surface potentials

  • Rupert L. Frank

    Caltech, Pasadena, United States
Eigenvalues of Schrödinger operators with complex surface potentials cover
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Abstract

We consider Schrödinger operators in Rd\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 LpL^p norm of the potential with d1<pdd-1 < p \leq d. We also prove bounds on sums of powers of eigenvalues.