{"title":"对正弦加法公式的扩展积分","authors":"M. Tial","doi":"10.23939/mmc2023.03.833","DOIUrl":null,"url":null,"abstract":"In this paper, we determine the continuous solutions of the integral functional equation of Stetkær's extension of the sine addition law ∫Gf(xyt)dμ(t)=f(x)χ1(y)+χ2(x)f(y), x,y∈G, where f:G→C, G is a locally compact Hausdorff group, μ is a regular, compactly supported, complex-valued Borel measure on G and χ1, χ2 are fixed characters on G.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Integral of an extension of the sine addition formula\",\"authors\":\"M. Tial\",\"doi\":\"10.23939/mmc2023.03.833\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we determine the continuous solutions of the integral functional equation of Stetkær's extension of the sine addition law ∫Gf(xyt)dμ(t)=f(x)χ1(y)+χ2(x)f(y), x,y∈G, where f:G→C, G is a locally compact Hausdorff group, μ is a regular, compactly supported, complex-valued Borel measure on G and χ1, χ2 are fixed characters on G.\",\"PeriodicalId\":37156,\"journal\":{\"name\":\"Mathematical Modeling and Computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Modeling and Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.23939/mmc2023.03.833\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Modeling and Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23939/mmc2023.03.833","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Integral of an extension of the sine addition formula
In this paper, we determine the continuous solutions of the integral functional equation of Stetkær's extension of the sine addition law ∫Gf(xyt)dμ(t)=f(x)χ1(y)+χ2(x)f(y), x,y∈G, where f:G→C, G is a locally compact Hausdorff group, μ is a regular, compactly supported, complex-valued Borel measure on G and χ1, χ2 are fixed characters on G.
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