Quantitative version of Weyl’s law

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2023-08-20 DOI:10.1007/s10455-023-09922-z

Nikhil Savale

引用次数: 0

Abstract

We prove a general estimate for the Weyl remainder of an elliptic, semiclassical pseudodifferential operator in terms of volumes of recurrence sets for the Hamilton flow of its principal symbol. This quantifies earlier results of Volovoy (Comm Partial Differential Equations 15:1509–1563, 1990; Ann Global Anal Geom 8:127–136, 1990). Our result particularly improves Weyl remainder exponents for compact Lie groups and surfaces of revolution. And gives a quantitative estimate for Bérard’s Weyl remainder in terms of the maximal expansion rate and topological entropy of the geodesic flow.

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魏尔定律的定量版本

我们用主符号Hamilton流的递推集的体积证明了半经典拟微分算子的Weyl余数的一般估计。这量化了Volovoy的早期结果（Comm偏微分方程15:1509-15631990；Ann Global Anal Geom 8:127-1361990）。我们的结果特别改进了紧致李群和公转曲面的Weyl余数指数。并根据测地流的最大展开率和拓扑熵，给出了Bérard的Weyl余数的定量估计。

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

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.