不连续函数类中的Radon变换反演公式

IF 0.58 Q3 Engineering

Journal of Applied and Industrial Mathematics Pub Date : 2024-12-01 DOI:10.1134/S1990478924030013

D. S. Anikonov, D. S. Konovalova

{"title":"不连续函数类中的Radon变换反演公式","authors":"D. S. Anikonov, D. S. Konovalova","doi":"10.1134/S1990478924030013","DOIUrl":null,"url":null,"abstract":"<p> We introduce the concept of a pseudoconvex set in an odd-dimensional Euclidean space.\nThe inversion formula is obtained for the Radon transform in the case where the integrand is a\npiecewise continuous function defined on a pseudoconvex set. The result achieved is\na generalization of a previously known property proved for smooth functions.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 3","pages":"379 - 383"},"PeriodicalIF":0.5800,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Radon Transform Inversion Formula in the Class\\nof Discontinuous Functions\",\"authors\":\"D. S. Anikonov, D. S. Konovalova\",\"doi\":\"10.1134/S1990478924030013\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> We introduce the concept of a pseudoconvex set in an odd-dimensional Euclidean space.\\nThe inversion formula is obtained for the Radon transform in the case where the integrand is a\\npiecewise continuous function defined on a pseudoconvex set. The result achieved is\\na generalization of a previously known property proved for smooth functions.\\n</p>\",\"PeriodicalId\":607,\"journal\":{\"name\":\"Journal of Applied and Industrial Mathematics\",\"volume\":\"18 3\",\"pages\":\"379 - 383\"},\"PeriodicalIF\":0.5800,\"publicationDate\":\"2024-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied and Industrial Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1990478924030013\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924030013","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}

引用次数: 0

摘要

在奇维欧几里德空间中引入了伪凸集的概念。得到了当被积函数是定义在伪凸集上的连续函数时Radon变换的反演公式。这个结果是对光滑函数的一个已知性质的推广。

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

Radon Transform Inversion Formula in the Class of Discontinuous Functions

We introduce the concept of a pseudoconvex set in an odd-dimensional Euclidean space. The inversion formula is obtained for the Radon transform in the case where the integrand is a piecewise continuous function defined on a pseudoconvex set. The result achieved is a generalization of a previously known property proved for smooth functions.

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

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.