{"title":"连续调制小剪切变换的定性不确定性原理","authors":"Piyush Bansal, Ajay Kumar, Ashish Bansal","doi":"10.1007/s43036-024-00346-5","DOIUrl":null,"url":null,"abstract":"<div><p>We prove the qualitative uncertainty principle for the continuous modulated shearlet transform on several classes of groups including Abelian groups, compact extensions of Abelian groups and Heisenberg group. As particular cases, one obtains the qualitative uncertainty principles for the Gabor transform, the wavelet transform and the shearlet transform.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Qualitative uncertainty principle for continuous modulated shearlet transform\",\"authors\":\"Piyush Bansal, Ajay Kumar, Ashish Bansal\",\"doi\":\"10.1007/s43036-024-00346-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove the qualitative uncertainty principle for the continuous modulated shearlet transform on several classes of groups including Abelian groups, compact extensions of Abelian groups and Heisenberg group. As particular cases, one obtains the qualitative uncertainty principles for the Gabor transform, the wavelet transform and the shearlet transform.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"9 3\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-05-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-024-00346-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-024-00346-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Qualitative uncertainty principle for continuous modulated shearlet transform
We prove the qualitative uncertainty principle for the continuous modulated shearlet transform on several classes of groups including Abelian groups, compact extensions of Abelian groups and Heisenberg group. As particular cases, one obtains the qualitative uncertainty principles for the Gabor transform, the wavelet transform and the shearlet transform.
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