 0958 Xue Ping Wang
 Number of eigenvalues for a class of nonselfadjoint Schr dinger operators
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Apr 3, 09

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Abstract. In this article, we prove the finiteness of the number of eigenvalues for a class of Schr\"odinger operators $H = \Delta + V(x)$ with a complexvalued potential $V(x)$ on $\bR^n$, $n \ge 2$. If $\Im V$ is sufficiently small, $\Im V \le 0$ and $\Im V \neq 0$, 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.
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