用矩阵理论分类奇阶微分算子的自伴随域

IF 0.9 4区数学 Q1 MATHEMATICS

Open Mathematics Pub Date : 2023-01-01 DOI:10.1515/math-2023-0104

Mao-zhu Zhang, Xiaoling Hao, Jing Wang

{"title":"用矩阵理论分类奇阶微分算子的自伴随域","authors":"Mao-zhu Zhang, Xiaoling Hao, Jing Wang","doi":"10.1515/math-2023-0104","DOIUrl":null,"url":null,"abstract":"Abstract In this article, we investigate the classification of self-adjoint boundary conditions of odd-order differential operators. We obtain that for odd-order self-adjoint boundary conditions under some assumptions, there are exactly two basic types of self-adjoint boundary conditions: coupled and mixed. Moreover we determine the number of possible conditions for each type, which is different from the even-order cases. Our construction will play an important role in the canonical forms and in the spectral analysis of these operators.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Classification of self-adjoint domains of odd-order differential operators with matrix theory\",\"authors\":\"Mao-zhu Zhang, Xiaoling Hao, Jing Wang\",\"doi\":\"10.1515/math-2023-0104\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this article, we investigate the classification of self-adjoint boundary conditions of odd-order differential operators. We obtain that for odd-order self-adjoint boundary conditions under some assumptions, there are exactly two basic types of self-adjoint boundary conditions: coupled and mixed. Moreover we determine the number of possible conditions for each type, which is different from the even-order cases. Our construction will play an important role in the canonical forms and in the spectral analysis of these operators.\",\"PeriodicalId\":48713,\"journal\":{\"name\":\"Open Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Open Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/math-2023-0104\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Open Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/math-2023-0104","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要本文研究了奇阶微分算子的自伴边界条件的分类。我们得到了在某些假设条件下，对于奇阶自伴边界条件，恰好存在两种基本类型的自伴随边界条件：耦合和混合。此外，我们确定了每种类型的可能条件的数量，这与偶数阶情况不同。我们的构造将在正则形式和这些算子的谱分析中发挥重要作用。

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

Classification of self-adjoint domains of odd-order differential operators with matrix theory

Abstract In this article, we investigate the classification of self-adjoint boundary conditions of odd-order differential operators. We obtain that for odd-order self-adjoint boundary conditions under some assumptions, there are exactly two basic types of self-adjoint boundary conditions: coupled and mixed. Moreover we determine the number of possible conditions for each type, which is different from the even-order cases. Our construction will play an important role in the canonical forms and in the spectral analysis of these operators.

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

Open Mathematics MATHEMATICS-

CiteScore

2.40

自引率

5.90%

发文量

审稿时长

16 weeks

期刊介绍： Open Mathematics - formerly Central European Journal of Mathematics Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication. Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind. Aims and Scope The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes: