{"title":"分数傅里叶变换的一般化及其分析特性","authors":"Yue Zhou","doi":"arxiv-2409.11201","DOIUrl":null,"url":null,"abstract":"We consider one-parameter families of quadratic-phase integral transforms\nwhich generalize the fractional Fourier transform. Under suitable regularity\nassumptions, we characterize the one-parameter groups formed by such\ntransforms. Necessary and sufficient conditions for continuous dependence on\nthe parameter are obtained in L2, pointwise, and almost-everywhere senses.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"66 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalizations of the fractional Fourier transform and their analytic properties\",\"authors\":\"Yue Zhou\",\"doi\":\"arxiv-2409.11201\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider one-parameter families of quadratic-phase integral transforms\\nwhich generalize the fractional Fourier transform. Under suitable regularity\\nassumptions, we characterize the one-parameter groups formed by such\\ntransforms. Necessary and sufficient conditions for continuous dependence on\\nthe parameter are obtained in L2, pointwise, and almost-everywhere senses.\",\"PeriodicalId\":501038,\"journal\":{\"name\":\"arXiv - MATH - Representation Theory\",\"volume\":\"66 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Representation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11201\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11201","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Generalizations of the fractional Fourier transform and their analytic properties
We consider one-parameter families of quadratic-phase integral transforms
which generalize the fractional Fourier transform. Under suitable regularity
assumptions, we characterize the one-parameter groups formed by such
transforms. Necessary and sufficient conditions for continuous dependence on
the parameter are obtained in L2, pointwise, and almost-everywhere senses.
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