{"title":"GLOBAL HYPOELLIPTICITY OF SUMS OF SQUARES ON COMPACT MANIFOLDS","authors":"Gabriel Araújo, Igor A. Ferra, Luis F. Ragognette","doi":"10.1017/s147474802300049x","DOIUrl":null,"url":null,"abstract":"<p>We present necessary and sufficient conditions for an operator of the type sum of squares to be globally hypoelliptic on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240105043019850-0091:S147474802300049X:S147474802300049X_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$T \\times G$</span></span></img></span></span>, where <span>T</span> is a compact Riemannian manifold and <span>G</span> is a compact Lie group. These conditions involve the global hypoellipticity of a system of vector fields on <span>G</span> and are weaker than Hörmander’s condition, while generalizing the well known Diophantine conditions on the torus. Examples of operators satisfying these conditions in the general setting are provided.</p>","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"52 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Institute of Mathematics of Jussieu","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s147474802300049x","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We present necessary and sufficient conditions for an operator of the type sum of squares to be globally hypoelliptic on $T \times G$, where T is a compact Riemannian manifold and G is a compact Lie group. These conditions involve the global hypoellipticity of a system of vector fields on G and are weaker than Hörmander’s condition, while generalizing the well known Diophantine conditions on the torus. Examples of operators satisfying these conditions in the general setting are provided.
期刊介绍：
The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.
$T \times G$, where T is a compact Riemannian manifold and G is a compact Lie group. These conditions involve the global hypoellipticity of a system of vector fields on G and are weaker than Hörmander’s condition, while generalizing the well known Diophantine conditions on the torus. Examples of operators satisfying these conditions in the general setting are provided.
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