09-58 Xue Ping Wang
Number of eigenvalues for a class of non-selfadjoint Schr dinger operators (348K, pdf) 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 complex-valued 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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