论文标题
关于一维非自我的雅各比和schr {\“ o} dinger操作员
On Lieb--Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schr{\" o}dinger operators
论文作者
论文摘要
我们研究了在多大程度上 - 不平等现象可以从自我伴侣到一般（可能是非自我偶像）雅各比（Jacobi）和施罗德（Schrödinger）操作员。也就是说，我们证明了[复杂肛门的汉斯曼和卡特里尔的猜想。操作。理论5，第1号（2011），197-218]，回答了其中提出的另一个开放问题。结果是通过对具有矩形屏障潜力和复杂耦合的离散schrödinger运算符的特征值的渐近分析获得的。在连续的环境中运用这些想法，我们还为一维的schrödinger运营商解决了类似的开放问题，该操作员在[Integral方程式理论75，No. 1（2013），1-5]中在Demuth，Hansmann和Katriel发表的复杂潜在潜力。
We study to what extent Lieb--Thirring inequalities are extendable from self-adjoint to general (possibly non-self-adjoint) Jacobi and Schrödinger operators. Namely, we prove the conjecture of Hansmann and Katriel from [Complex Anal. Oper. Theory 5, No. 1 (2011), 197-218] and answer another open question raised therein. The results are obtained by means of asymptotic analysis of eigenvalues of discrete Schrödinger operators with rectangular barrier potential and complex coupling. Applying the ideas in the continuous setting, we also solve a similar open problem for one-dimensional Schrödinger operators with complex-valued potentials published by Demuth, Hansmann, and Katriel in [Integral Equations Operator Theory 75, No. 1 (2013), 1-5].
