The spectral determinant for second-order elliptic operators on the real line

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2024-05-23 DOI:10.1007/s11005-024-01819-7

Pedro Freitas, Jiří Lipovský

引用次数: 0

Abstract

We derive an expression for the spectral determinant of a second-order elliptic differential operator \( \mathcal {T} \) defined on the whole real line, in terms of the Wronskians of two particular solutions of the equation \( \mathcal {T} u=0\). Examples of application of the resulting formula include the explicit calculation of the determinant of harmonic and anharmonic oscillators with an added bounded potential with compact support.

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实线上二阶椭圆算子的谱行列式

我们根据方程 \( \mathcal {T} u=0\) 两个特定解的弗伦斯基，推导出定义在整个实线上的二阶椭圆微分算子 \( \mathcal {T} \) 的谱行列式表达式。所得公式的应用实例包括明确计算带有紧凑支持的有界势的谐和振荡器和非谐和振荡器的行列式。

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

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.