{"title":"p进傅里叶变换","authors":"G.F. Borm","doi":"10.1016/1385-7258(88)90001-7","DOIUrl":null,"url":null,"abstract":"<div><p>In [3]-[7] Woodcock developed a Fourier theory for continuously differentiable functions defined on the set of p-adic integers. In this paper his theory is continued by giving a characterization of the image of the Fourier transformation. Also a special form of continuity of the inverse Fourier transformation is proved and, as an application, the Fourier transform of an antiderivative of a function is calculated.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 1","pages":"Pages 1-8"},"PeriodicalIF":0.0000,"publicationDate":"1988-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/1385-7258(88)90001-7","citationCount":"0","resultStr":"{\"title\":\"p-adic Fourier transforms\",\"authors\":\"G.F. Borm\",\"doi\":\"10.1016/1385-7258(88)90001-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In [3]-[7] Woodcock developed a Fourier theory for continuously differentiable functions defined on the set of p-adic integers. In this paper his theory is continued by giving a characterization of the image of the Fourier transformation. Also a special form of continuity of the inverse Fourier transformation is proved and, as an application, the Fourier transform of an antiderivative of a function is calculated.</p></div>\",\"PeriodicalId\":100664,\"journal\":{\"name\":\"Indagationes Mathematicae (Proceedings)\",\"volume\":\"91 1\",\"pages\":\"Pages 1-8\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1988-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/1385-7258(88)90001-7\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indagationes Mathematicae (Proceedings)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/1385725888900017\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/1385725888900017","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In [3]-[7] Woodcock developed a Fourier theory for continuously differentiable functions defined on the set of p-adic integers. In this paper his theory is continued by giving a characterization of the image of the Fourier transformation. Also a special form of continuity of the inverse Fourier transformation is proved and, as an application, the Fourier transform of an antiderivative of a function is calculated.
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