{"title":"Duality Property of Two-Sided Quaternion Fourier Transform","authors":"M. Bahri, R. Ashino","doi":"10.1109/ICWAPR.2018.8521310","DOIUrl":null,"url":null,"abstract":"An alternative proof of scalar Parseval's formula with respect to the two-sided quaternion Fourier transform is presented. It is shown that the inverse of the two-sided quaternion Fourier transform is continuous and bounded on R 2. The duality property of the two-sided quaternion Fourier transform is established. The alternative form of the Hausdorff-Young inequality associated with the two-sided quaternion Fourier transform is expressed. AMS Subject Classification: 11R52, 42A38, 15A66","PeriodicalId":385478,"journal":{"name":"2018 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)","volume":"181 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2018 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICWAPR.2018.8521310","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
An alternative proof of scalar Parseval's formula with respect to the two-sided quaternion Fourier transform is presented. It is shown that the inverse of the two-sided quaternion Fourier transform is continuous and bounded on R 2. The duality property of the two-sided quaternion Fourier transform is established. The alternative form of the Hausdorff-Young inequality associated with the two-sided quaternion Fourier transform is expressed. AMS Subject Classification: 11R52, 42A38, 15A66
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