全实线上一维薛定谔算子的优化反谱问题

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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