{"title":"统一度量和 q-Dunkl 傅立叶变换中的广义 Lipschitz 类","authors":"Sergey Volosivets","doi":"10.1007/s13324-024-00983-2","DOIUrl":null,"url":null,"abstract":"<div><p>For a function defined on <span>\\({\\mathbb {R}}_q\\)</span> we define two new variants of a modulus of smoothness and give a Boas type result about connection between the smoothness of this function and the behavior of its q-Dunkle Fourier transform near zero and at infinity.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalized Lipschitz classes in uniform metric and q-Dunkl Fourier transforms\",\"authors\":\"Sergey Volosivets\",\"doi\":\"10.1007/s13324-024-00983-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For a function defined on <span>\\\\({\\\\mathbb {R}}_q\\\\)</span> we define two new variants of a modulus of smoothness and give a Boas type result about connection between the smoothness of this function and the behavior of its q-Dunkle Fourier transform near zero and at infinity.</p></div>\",\"PeriodicalId\":48860,\"journal\":{\"name\":\"Analysis and Mathematical Physics\",\"volume\":\"14 6\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-10-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis and Mathematical Physics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13324-024-00983-2\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s13324-024-00983-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Generalized Lipschitz classes in uniform metric and q-Dunkl Fourier transforms
For a function defined on \({\mathbb {R}}_q\) we define two new variants of a modulus of smoothness and give a Boas type result about connection between the smoothness of this function and the behavior of its q-Dunkle Fourier transform near zero and at infinity.
期刊介绍：
Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.
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