arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1210.7628math.SPmath-phmath.MP
收藏

具有分布势的Sturm-Liouville算子的逆Spectral Theory

Inverse Spectral Theory for Sturm-Liouville Operators with Distributional Potentials

Jonathan Eckhardt, Fritz Gesztesy, Roger Nichols, Gerald Teschl

备注：
29 pages
发表信息：
J. Lond. Math. Soc. (2) 88, 801-828 (2013)
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

本文讨论了任意区间上奇异微分算子的逆谱理论，其中系数$(a,b) \subseteq \mathbb{R}$，$q$，$r$，$s$在$(a,b)$上是Lebesgue可测的，且具有$p\not=0$，$q$，$r$，$r>0$;在$(a,b)$上。特别是，我们明确允许某些分布势系数。本文导出的逆谱理论结果包括谱测度、双谱和三谱以及局部Borg-Marchenko型逆谱结果。特别地，孤立了具有分布势的薛定谔算子和阻抗形式的Sturm-Liouville算子的特殊情况。

英文摘要：

We discuss inverse spectral theory for singular differential operators on arbitrary intervals $(a,b) \subseteq \mathbb{R}$ associated with rather general differential expressions of the type \[τf = \frac{1}{r} \left(- \big(p[f' + s f]\big)' + s p[f' + s f] + qf\right), \] where the coefficients $p$, $q$, $r$, $s$ are Lebesgue measurable on $(a,b)$ with $p^{-1}$, $q$, $r$, $s \in L^1_{\text{loc}}((a,b); dx)$ and real-valued with $p\not=0$ and $r>0$ a.e.\ on $(a,b)$. In particular, we explicitly permit certain distributional potential coefficients. The inverse spectral theory results derived in this paper include those implied by the spectral measure, by two-spectra and three-spectra, as well as local Borg-Marchenko-type inverse spectral results. The special cases of Schrödinger operators with distributional potentials and Sturm--Liouville operators in impedance form are isolated, in particular.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑