{"title":"奇异函数 rngs 的代数结果","authors":"Arran Fernandez, Müge Saadetoğlu","doi":"10.1515/forum-2023-0445","DOIUrl":null,"url":null,"abstract":"We consider a Mikusiński-type convolution algebra <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>C</m:mi> <m:mi>α</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0445_eq_0144.png\" /> <jats:tex-math>{C_{\\alpha}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, including functions with power-type singularities at the origin as well as all functions continuous on <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo stretchy=\"false\">[</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mi mathvariant=\"normal\">∞</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0445_eq_0198.png\" /> <jats:tex-math>{[0,\\infty)}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Algebraic properties of this space are derived, including its ideal structure, filtered and graded structure, and Jacobson radical. Applications to operators of fractional calculus and the associated integro-differential equations are discussed.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"37 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algebraic results on rngs of singular functions\",\"authors\":\"Arran Fernandez, Müge Saadetoğlu\",\"doi\":\"10.1515/forum-2023-0445\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a Mikusiński-type convolution algebra <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msub> <m:mi>C</m:mi> <m:mi>α</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_forum-2023-0445_eq_0144.png\\\" /> <jats:tex-math>{C_{\\\\alpha}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, including functions with power-type singularities at the origin as well as all functions continuous on <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mrow> <m:mo stretchy=\\\"false\\\">[</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mi mathvariant=\\\"normal\\\">∞</m:mi> <m:mo stretchy=\\\"false\\\">)</m:mo> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_forum-2023-0445_eq_0198.png\\\" /> <jats:tex-math>{[0,\\\\infty)}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Algebraic properties of this space are derived, including its ideal structure, filtered and graded structure, and Jacobson radical. Applications to operators of fractional calculus and the associated integro-differential equations are discussed.\",\"PeriodicalId\":12433,\"journal\":{\"name\":\"Forum Mathematicum\",\"volume\":\"37 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-01-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Forum Mathematicum\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/forum-2023-0445\",\"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":"Forum Mathematicum","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/forum-2023-0445","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We consider a Mikusiński-type convolution algebra Cα{C_{\alpha}}, including functions with power-type singularities at the origin as well as all functions continuous on [0,∞){[0,\infty)}. Algebraic properties of this space are derived, including its ideal structure, filtered and graded structure, and Jacobson radical. Applications to operators of fractional calculus and the associated integro-differential equations are discussed.
期刊介绍：
Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.
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