On Lieb–Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators

IF 1 3区数学 Q1 MATHEMATICS Journal of Spectral Theory Pub Date : 2020-04-21 DOI:10.4171/jst/378

Sabine Bogli, F. vStampach

引用次数: 10

Abstract

We study to what extent Lieb--Thirring inequalities are extendable from self-adjoint to general (possibly non-self-adjoint) Jacobi and Schrodinger 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 Schrodinger 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 Schrodinger operators with complex-valued potentials published by Demuth, Hansmann, and Katriel in [Integral Equations Operator Theory 75, No. 1 (2013), 1-5].

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一维非自伴随Jacobi算子和Schrödinger算子的Lieb-Thirring不等式

我们研究了Lieb—Thirring不等式从自伴随扩展到一般(可能是非自伴随的)Jacobi和Schrodinger算子的程度。即从[Complex Anal]证明了Hansmann和Katriel的猜想。③。理论5,No. 1(2011)， 197-218]并回答其中提出的另一个开放性问题。通过对具有矩形势垒和复耦合的离散薛定谔算子特征值的渐近分析，得到了上述结果。将这些思想应用于连续设置，我们还解决了Demuth, Hansmann和Katriel在[积分方程算子理论75,No. 1(2013)， 1-5]中发表的具有复值势的一维薛定谔算子的类似开放问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Spectral Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： The Journal of Spectral Theory is devoted to the publication of research articles that focus on spectral theory and its many areas of application. Articles of all lengths including surveys of parts of the subject are very welcome. The following list includes several aspects of spectral theory and also fields which feature substantial applications of (or to) spectral theory. Schrödinger operators, scattering theory and resonances; eigenvalues: perturbation theory, asymptotics and inequalities; quantum graphs, graph Laplacians; pseudo-differential operators and semi-classical analysis; random matrix theory; the Anderson model and other random media; non-self-adjoint matrices and operators, including Toeplitz operators; spectral geometry, including manifolds and automorphic forms; linear and nonlinear differential operators, especially those arising in geometry and physics; orthogonal polynomials; inverse problems.