Eigenvalue bounds for Schrödinger operators with complex potentials on compact manifolds

Abstract

We prove eigenvalue bounds for Schrödinger operator $-{\Delta }_g+V$ on compact manifolds with complex potentials $V$. The bounds depend only on an $L^q$-norm of the potential, and they are shown to be optimal, in a certain sense, on the round sphere and more general Zoll manifolds. These bounds are natural analogues of Frank's \cite{MR2820160} results in the Euclidean case.

21 pages; minor misprints corrected

References in corpus (1)

• Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces