Approximation of Dirac operators with δ ${\delta }$ -shell potentials in the norm resolvent sense. I. Qualitative results

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-07-27 DOI:10.1002/mana.70004

Jussi Behrndt, Markus Holzmann, Christian Stelzer-Landauer

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引用次数: 0

Abstract

In this paper, the approximation of Dirac operators with general $δ$ -shell potentials supported on $C^{2}$ -curves in $R^{2}$ or $C^{2}$ -surfaces in $R^{3}$ , which may be bounded or unbounded, is studied. It is shown under suitable conditions on the weight of the $δ$ -interaction that a family of Dirac operators with regular, squeezed potentials converges in the norm resolvent sense to the Dirac operator with the $δ$ -shell interaction.

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范数解析意义上δ ${\delta}$壳势的Dirac算子逼近。一、定性结果

在本文中，具有一般δ $\ δ $壳层势的Dirac算子在r2 $\mathbb {R}^2$或c2 $C^2$曲线上的近似研究了r3 $\mathbb {R}^3$中的c2 $C^2$ -曲面，它可以是有界的，也可以是无界的。在δ $\ δ $ -相互作用权值的适当条件下，具有正则压缩势的狄拉克算子族在范数解析意义上收敛于具有δ $\ δ $ -壳相互作用的狄拉克算子族。

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

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index