没有完全正则性的$${mathbb {R}}^d$$ 上局部磁薛定谔算子的尖锐半经典谱渐近学

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2024-07-16 DOI:10.1007/s00023-024-01471-w

Søren Mikkelsen

引用次数: 0

摘要

我们考虑作用于$L^2({\mathbb {R}}^d)$和$d\ge 3$中的算符，它们在局部表现为磁性Schrödinger算符。对于磁性Schrödinger算子，我们假设磁势是光滑的，电势是五倍可微的，五阶导数是Hölder连续的。在这些假设下，我们建立了局部计数函数和Riesz均值的尖锐谱渐近性。

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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Sharp Semiclassical Spectral Asymptotics for Local Magnetic Schrödinger Operators on ${\mathbb {R}}^d$ Without Full Regularity

We consider operators acting in $L^2({\mathbb {R}}^d)$ with $d\ge 3$ that locally behave as a magnetic Schrödinger operator. For the magnetic Schrödinger operators, we suppose the magnetic potentials are smooth and the electric potential is five times differentiable and the fifth derivatives are Hölder continuous. Under these assumptions, we establish sharp spectral asymptotics for localised counting functions and Riesz means.

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来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.