Number of eigenvalues for a class of non-selfadjoint Schrödinger operators

Abstract

In this article, we prove the finiteness of the number of eigenvalues for a class of Schrödinger operators $H=-\Delta +V(x)$ with a complex-valued potential $V(x)$ on $\bR^n$, $n\ge 2$. If $\Im V$ is sufficiently small, $\Im V\le 0$ and $\Im V\ne 0$, we show that $N(V)=N(\Re V)+k$, where $k$ is the multiplicity of the zero resonance of the selfadjoint operator $-\Delta +\Re V$ and $N(W)$ the number of eigenvalues of $-\Delta +W$, counted according to their algebraic multiplicity.

19 pages

References in corpus (5)

• Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
• Limiting absorption principle for the dissipative Helmholtz equation
• On the discrete spectrum of complex banded matrices
• Counting Schrödinger boundstates: semiclassics and beyond
• On limit sets for the discrete spectrum of complex Jacobi matrices

Cited by in corpus (3)

• Limiting absorption principle for some long range perturbations of Dirac systems at threshold energies
• A criterion for the existence of non-real eigenvalues for a Dirac operator
• Spectral non-self-adjoint analysis of complex Dirac, Pauli and Schrödinger operators of full rank with constant magnetic fields