全实线上一维薛定谔算子的优化反谱问题

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2024-07-30 DOI:10.1134/s0012266124040050

V. A. Sadovnichii, Ya. T. Sultanaev, N. F. Valeev

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引用次数: 0

摘要

摘要我们研究了一维薛定谔算子在整轴上具有不完整谱数据的优化逆谱问题的陈述：对于给定的势\(q_0 \)，找到最接近的函数\(\hat {q} \)，使得具有势\(\hat {q}\)的薛定谔算子的第一个特征值与给定值\(\lambda _k^*\in \mathbb {R} \)，\(k={1,\dots ,m}\)重合。

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Optimization Inverse Spectral Problem for the One-Dimensional Schrödinger Operator on the Entire Real Line

Abstract

We study the statement of the optimization inverse spectral problem with incomplete spectral data for the one-dimensional Schrödinger operator on the entire axis: for a given potential \(q_0 \), find the closest function \(\hat {q} \) such that the first \(m \) eigenvalues of the Schrödinger operator with potential \(\hat {q}\) coincide with given values \(\lambda _k^*\in \mathbb {R} \), \(k={1,\dots ,m}\).

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.