{"title":"环面上一类实向量场系统的正则性传播","authors":"I.A. Ferra, L.A. Carvalho dos Santos","doi":"10.1016/j.jfa.2024.110807","DOIUrl":null,"url":null,"abstract":"<div><div>We characterize the global hypoellipticity, almost hypoellipticity and solvability for a class of systems of real vector fields on the <span><math><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-dimensional torus as well as the same properties about the sum of squares associated to the system. The key result is a theorem about propagation of regularity for solutions of the system.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 6","pages":"Article 110807"},"PeriodicalIF":1.6000,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Propagation of regularity for a class of systems of real vector fields on torus\",\"authors\":\"I.A. Ferra, L.A. Carvalho dos Santos\",\"doi\":\"10.1016/j.jfa.2024.110807\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We characterize the global hypoellipticity, almost hypoellipticity and solvability for a class of systems of real vector fields on the <span><math><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-dimensional torus as well as the same properties about the sum of squares associated to the system. The key result is a theorem about propagation of regularity for solutions of the system.</div></div>\",\"PeriodicalId\":15750,\"journal\":{\"name\":\"Journal of Functional Analysis\",\"volume\":\"288 6\",\"pages\":\"Article 110807\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2025-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022123624004956\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/1/6 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022123624004956","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/6 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Propagation of regularity for a class of systems of real vector fields on torus
We characterize the global hypoellipticity, almost hypoellipticity and solvability for a class of systems of real vector fields on the -dimensional torus as well as the same properties about the sum of squares associated to the system. The key result is a theorem about propagation of regularity for solutions of the system.
期刊介绍：
The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published.
Research Areas Include:
• Significant applications of functional analysis, including those to other areas of mathematics
• New developments in functional analysis
• Contributions to important problems in and challenges to functional analysis
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