{"title":"𝑞-sided卷积型齐次方程的一般初等解","authors":"Yuriy Saranchuk, A. Shishkin","doi":"10.1090/spmj/1774","DOIUrl":null,"url":null,"abstract":"Exponential polynomials satisfying a homogeneous equation of convolution type are called its elementary solutions. The article is devoted to convolution-type operators in the complex domain that generalize the well-known operators of \n\n \n q\n q\n \n\n-sided convolution and \n\n \n π\n \\pi\n \n\n-convolution. The properties of such operators are investigated and the general form of elementary solutions (general elementary solution) of a homogeneous equation of \n\n \n q\n q\n \n\n-sided convolution type is described.","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"General elementary solution of a 𝑞-sided convolution type homogeneous equation\",\"authors\":\"Yuriy Saranchuk, A. Shishkin\",\"doi\":\"10.1090/spmj/1774\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Exponential polynomials satisfying a homogeneous equation of convolution type are called its elementary solutions. The article is devoted to convolution-type operators in the complex domain that generalize the well-known operators of \\n\\n \\n q\\n q\\n \\n\\n-sided convolution and \\n\\n \\n π\\n \\\\pi\\n \\n\\n-convolution. The properties of such operators are investigated and the general form of elementary solutions (general elementary solution) of a homogeneous equation of \\n\\n \\n q\\n q\\n \\n\\n-sided convolution type is described.\",\"PeriodicalId\":51162,\"journal\":{\"name\":\"St Petersburg Mathematical Journal\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-07-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"St Petersburg Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/spmj/1774\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/spmj/1774","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
General elementary solution of a 𝑞-sided convolution type homogeneous equation
Exponential polynomials satisfying a homogeneous equation of convolution type are called its elementary solutions. The article is devoted to convolution-type operators in the complex domain that generalize the well-known operators of
q
q
-sided convolution and
π
\pi
-convolution. The properties of such operators are investigated and the general form of elementary solutions (general elementary solution) of a homogeneous equation of
q
q
-sided convolution type is described.
期刊介绍：
This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.
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