环境（欧几里得）坐标正交群上的拉普拉斯-贝尔特拉米算子

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2023-12-12 DOI:10.1016/j.acha.2023.101619

Petre Birtea, Ioan Caşu, Dan Comănescu

{"title":"环境（欧几里得）坐标正交群上的拉普拉斯-贝尔特拉米算子","authors":"Petre Birtea, Ioan Caşu, Dan Comănescu","doi":"10.1016/j.acha.2023.101619","DOIUrl":null,"url":null,"abstract":"<div>Using the embedded gradient vector field method (see P. Birtea, D. Comănescu (2015) [7]), we present a general formula for the Laplace-Beltrami operator defined on a constraint manifold, written in the ambient coordinates. Regarding the orthogonal group as a constraint submanifold of the Euclidean space of <math><mi>n</mi><mo>×</mo><mi>n</mi></math> matrices, we give an explicit formula for the Laplace-Beltrami operator on the orthogonal group using the ambient Euclidean coordinates. We apply this new formula for some relevant functions.</div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"69 ","pages":"Article 101619"},"PeriodicalIF":2.6000,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Laplace-Beltrami operator on the orthogonal group in ambient (Euclidean) coordinates\",\"authors\":\"Petre Birtea, Ioan Caşu, Dan Comănescu\",\"doi\":\"10.1016/j.acha.2023.101619\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>Using the embedded gradient vector field method (see P. Birtea, D. Comănescu (2015) [7]), we present a general formula for the Laplace-Beltrami operator defined on a constraint manifold, written in the ambient coordinates. Regarding the orthogonal group as a constraint submanifold of the Euclidean space of <math><mi>n</mi><mo>×</mo><mi>n</mi></math> matrices, we give an explicit formula for the Laplace-Beltrami operator on the orthogonal group using the ambient Euclidean coordinates. We apply this new formula for some relevant functions.</div>\",\"PeriodicalId\":55504,\"journal\":{\"name\":\"Applied and Computational Harmonic Analysis\",\"volume\":\"69 \",\"pages\":\"Article 101619\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2023-12-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied and Computational Harmonic Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1063520323001069\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied and Computational Harmonic Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1063520323001069","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

利用嵌入梯度矢量场方法（见 P. Birtea, D. Comănescu (2015) [7]），我们给出了在约束流形上定义的拉普拉斯-贝尔特拉米算子的一般公式，并以环境坐标写出。关于作为 n×n 矩阵欧几里得空间约束子流形的正交群，我们给出了使用环境欧几里得坐标的正交群上拉普拉斯-贝尔特拉米算子的明确公式。我们将这一新公式应用于一些相关函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Laplace-Beltrami operator on the orthogonal group in ambient (Euclidean) coordinates

Using the embedded gradient vector field method (see P. Birtea, D. Comănescu (2015) [7]), we present a general formula for the Laplace-Beltrami operator defined on a constraint manifold, written in the ambient coordinates. Regarding the orthogonal group as a constraint submanifold of the Euclidean space of $n \times n$ matrices, we give an explicit formula for the Laplace-Beltrami operator on the orthogonal group using the ambient Euclidean coordinates. We apply this new formula for some relevant functions.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.