A proof of a trace formula by Richard Melrose

IF 2.1 2区数学 Q1 MATHEMATICS

Advanced Nonlinear Studies Pub Date : 2022-05-18 DOI:10.1515/ans-2022-0054

Yves Colin de Verdière

引用次数: 1

Abstract

Abstract The goal of this article is to give a new proof of the wave trace formula proved by Richard Melrose in an impressive article. This trace formula is an extension of the Chazarain-Duistermaat-Guillemin trace formula (denoted as “CDG trace formula” in this article) to the case of a sub-Riemannian Laplacian on a 3D contact closed manifold. The proof uses a normal form constructed in previous papers, following the pioneering work of Melrose to reduce the case of the invariant Laplacian on the 3D-Heisenberg group. We need also the propagation of singularities results of the works of Ivrii, Lascar, and Melrose.

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理查德·梅尔罗斯对一个微量公式的证明

本文的目的是对Richard Melrose在一篇令人印象深刻的文章中证明的波迹公式给出一个新的证明。这个迹公式是Chazarain-Duistermaat-Guillemin迹公式（在本文中表示为“CDG迹公式”）在三维接触闭流形上的子黎曼拉普拉斯算子的情况下的推广。该证明使用了先前论文中构建的范式，遵循了Melrose的开创性工作，减少了三维海森堡群上不变拉普拉斯算子的情况。我们还需要Ivrii、Lascar和Melrose的奇异性传播结果。

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

Advanced Nonlinear Studies 数学-数学

CiteScore

3.00

自引率

5.60%

发文量

审稿时长

12 months

期刊介绍： Advanced Nonlinear Studies is aimed at publishing papers on nonlinear problems, particulalry those involving Differential Equations, Dynamical Systems, and related areas. It will also publish novel and interesting applications of these areas to problems in engineering and the sciences. Papers submitted to this journal must contain original, timely, and significant results. Articles will generally, but not always, be published in the order when the final copies were received.