{"title":"高自旋克利福德分析中的一些性质和积分变换","authors":"Chao Ding","doi":"arxiv-2409.09952","DOIUrl":null,"url":null,"abstract":"Rarita-Schwinger equation plays an important role in theoretical physics.\nBure\\v s et al. generalized it to arbitrary spin $k/2$ in 2002 in the context\nof Clifford algebras. In this article, we introduce the mean value property,\nCauchy's estimates, and Liouville's theorem for null solutions to\nRarita-Schwinger operator in Euclidean spaces. Further, we investigate\nboundednesses to the Teodorescu transform and its derivatives. This gives rise\nto a Hodge decomposition of an $L^2$ spaces in terms of the kernel space of the\nRarita-Schwinger operator and it also generalizes Bergman spaces in higher spin\ncases. \\end{abstract}","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"99 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some properties and integral transforms in higher spin Clifford analysis\",\"authors\":\"Chao Ding\",\"doi\":\"arxiv-2409.09952\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Rarita-Schwinger equation plays an important role in theoretical physics.\\nBure\\\\v s et al. generalized it to arbitrary spin $k/2$ in 2002 in the context\\nof Clifford algebras. In this article, we introduce the mean value property,\\nCauchy's estimates, and Liouville's theorem for null solutions to\\nRarita-Schwinger operator in Euclidean spaces. Further, we investigate\\nboundednesses to the Teodorescu transform and its derivatives. This gives rise\\nto a Hodge decomposition of an $L^2$ spaces in terms of the kernel space of the\\nRarita-Schwinger operator and it also generalizes Bergman spaces in higher spin\\ncases. \\\\end{abstract}\",\"PeriodicalId\":501142,\"journal\":{\"name\":\"arXiv - MATH - Complex Variables\",\"volume\":\"99 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Complex Variables\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09952\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09952","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
Bure\v s 等人于 2002 年在克利福德代数的背景下将其推广到任意自旋 $k/2$。在本文中,我们介绍了欧几里得空间中拉里塔-施文格算子空解的均值性质、考希估计和柳维尔定理。此外,我们还研究了 Teodorescu 变换及其导数的有界性。这就产生了以拉里塔-施文格算子的核空间为条件的 $L^2$ 空间的霍奇分解,而且它还概括了更高空间情况下的伯格曼空间。\结束语
Some properties and integral transforms in higher spin Clifford analysis
Rarita-Schwinger equation plays an important role in theoretical physics.
Bure\v s et al. generalized it to arbitrary spin $k/2$ in 2002 in the context
of Clifford algebras. In this article, we introduce the mean value property,
Cauchy's estimates, and Liouville's theorem for null solutions to
Rarita-Schwinger operator in Euclidean spaces. Further, we investigate
boundednesses to the Teodorescu transform and its derivatives. This gives rise
to a Hodge decomposition of an $L^2$ spaces in terms of the kernel space of the
Rarita-Schwinger operator and it also generalizes Bergman spaces in higher spin
cases. \end{abstract}