论文标题
扩张分析方法用于复杂的LIEB-裂纹类型估计的另一应用
Another Application of Dilation Analytic Method for Complex Lieb--Thirring Type Estimates
论文作者
论文摘要
我们考虑非自我添加schrödinger运算符$ h _ {\ rm c} = - δ+v _ {\ rm c} $（seves。真正的）潜力。我们能够在\ cite {so1}（n。sosyama，“非自我 - 亚偶像schrödingeroperators具有扩张分析复杂潜力的特征值的数量）中，我们能够找到扩张分析方法的新应用。我们在开放的复杂扇区中对$ h _ {\ rm c} $的共振特征值进行了lieb-类型的估计，并以\ cite {so1}的范围相同的方式在$ h _ {\ rm rm r} $的嵌入eigenvalues上进行eigenvalues。为了实现这一目标，我们得出了lieb-在几个复杂子领域的隔离特征值$ h $的局部类型不平等。
We consider non-self-adjoint Schrödinger operators $H_{\rm c}=-Δ+V_{\rm c}$ (resp. $H_{\rm r}=-Δ+V_{\rm r}$) acting in $L^2(\mathbb R^d)$, $d\ge 1$, with dilation analytic complex (resp. real) potentials. We were able to find out perhaps a new application of dilation analytic method in \cite{So1} (N. Someyama, "Number of Eigenvalues of Non-self-adjoint Schrödinger Operators with Dilation Analytic Complex Potentials," Reports on Mathematical Physics, Volume 83, Issue 2, pp.163-174 (2019).). We give a Lieb--Thirring type estimate on resonance eigenvalues of $H_{\rm c}$ in the open complex sector and that on embedded eigenvalues of $H_{\rm r}$ in the same way as \cite{So1}. To achieve that, we derive Lieb--Thirring type inequalities for isolated eigenvalues of $H$ on several complex subplanes.
