双边四元数傅里叶变换的对偶性

2018 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR) Pub Date : 2018-07-01 DOI:10.1109/ICWAPR.2018.8521310

M. Bahri, R. Ashino

{"title":"双边四元数傅里叶变换的对偶性","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":"{\"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}","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

摘要

给出了标量Parseval公式关于双边四元数傅里叶变换的另一种证明。证明了双边四元数傅里叶变换的逆是连续的，并且在r2上有界。建立了双边四元数傅里叶变换的对偶性质。与双边四元数傅里叶变换相关的Hausdorff-Young不等式的替代形式被表示。学科分类:11R52、42A38、15A66

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

Duality Property of Two-Sided Quaternion Fourier Transform

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

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

2018 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)

自引率

0.00%

发文量