{"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}
引用次数: 0
Abstract
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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