{"title":"洛伦兹反演与贝特曼变换之间的关系","authors":"Katsunori Shimomura","doi":"10.5036/MJIU.44.1","DOIUrl":null,"url":null,"abstract":"In our previous paper [1], we proved that every transformation which preserves the wave equation is a similarity or a Lorentzian inversion composed with similarities or a Bateman transformation composed with similarities. In this paper, we give several relations between Bateman transformation and Lorentzian inversion. We also prove that only Lorentzian inversion or Bateman transformation is enough to generate the set of all transformations which preserve the wave equation.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"65 1","pages":"1-5"},"PeriodicalIF":0.0000,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A relation between the Lorentzian inversion and the Bateman transformation\",\"authors\":\"Katsunori Shimomura\",\"doi\":\"10.5036/MJIU.44.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In our previous paper [1], we proved that every transformation which preserves the wave equation is a similarity or a Lorentzian inversion composed with similarities or a Bateman transformation composed with similarities. In this paper, we give several relations between Bateman transformation and Lorentzian inversion. We also prove that only Lorentzian inversion or Bateman transformation is enough to generate the set of all transformations which preserve the wave equation.\",\"PeriodicalId\":18362,\"journal\":{\"name\":\"Mathematical Journal of Ibaraki University\",\"volume\":\"65 1\",\"pages\":\"1-5\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Journal of Ibaraki University\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5036/MJIU.44.1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Journal of Ibaraki University","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5036/MJIU.44.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A relation between the Lorentzian inversion and the Bateman transformation
In our previous paper [1], we proved that every transformation which preserves the wave equation is a similarity or a Lorentzian inversion composed with similarities or a Bateman transformation composed with similarities. In this paper, we give several relations between Bateman transformation and Lorentzian inversion. We also prove that only Lorentzian inversion or Bateman transformation is enough to generate the set of all transformations which preserve the wave equation.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
