{"title":"广义v线变换的张量层析成像 \\(\\mathbb {R}^2\\)","authors":"Rahul Bhardwaj","doi":"10.1007/s13324-025-01088-0","DOIUrl":null,"url":null,"abstract":"<div><p>We study a set of generalized V-line transforms, namely longitudinal, mixed, and transverse V-line transforms, of a symmetric <i>m</i>-tensor field in <span>\\(\\mathbb {R}^2\\)</span>. The goal of this article is to recover a symmetric <i>m</i>-tensor field <span>\\({\\textbf {{f}}}\\)</span> supported in a disk <span>\\(\\mathbb {D}_R\\)</span>, with radius <i>R</i> and centered at the origin, by a combination of the aforementioned generalized V-line transforms, using two different techniques for different sets of data.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 4","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Tensor tomography for a set of generalized V-line transforms in \\\\(\\\\mathbb {R}^2\\\\)\",\"authors\":\"Rahul Bhardwaj\",\"doi\":\"10.1007/s13324-025-01088-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study a set of generalized V-line transforms, namely longitudinal, mixed, and transverse V-line transforms, of a symmetric <i>m</i>-tensor field in <span>\\\\(\\\\mathbb {R}^2\\\\)</span>. The goal of this article is to recover a symmetric <i>m</i>-tensor field <span>\\\\({\\\\textbf {{f}}}\\\\)</span> supported in a disk <span>\\\\(\\\\mathbb {D}_R\\\\)</span>, with radius <i>R</i> and centered at the origin, by a combination of the aforementioned generalized V-line transforms, using two different techniques for different sets of data.</p></div>\",\"PeriodicalId\":48860,\"journal\":{\"name\":\"Analysis and Mathematical Physics\",\"volume\":\"15 4\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2025-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis and Mathematical Physics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13324-025-01088-0\",\"RegionNum\":3,\"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":"Analysis and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s13324-025-01088-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Tensor tomography for a set of generalized V-line transforms in \(\mathbb {R}^2\)
We study a set of generalized V-line transforms, namely longitudinal, mixed, and transverse V-line transforms, of a symmetric m-tensor field in \(\mathbb {R}^2\). The goal of this article is to recover a symmetric m-tensor field \({\textbf {{f}}}\) supported in a disk \(\mathbb {D}_R\), with radius R and centered at the origin, by a combination of the aforementioned generalized V-line transforms, using two different techniques for different sets of data.
期刊介绍:
Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.