{"title":"指数型全函数模中主子模的若干性质及其在实轴上的多项式增长","authors":"N. Abuzyarova","doi":"10.13108/2016-8-1-1","DOIUrl":null,"url":null,"abstract":"In the work we consider a topological module of entire functions P(a; b), which is the isomorphic image of Fourier-Laplace transform of Schwarz space formed by distributions with compact supports in a finite or infinite segment (a; b) ⊂ R. We study the conditions ensuring that the principal submodule of module P(a; b) can be uniquely recovered by the zeroes of a generating function.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"34 1","pages":"3-12"},"PeriodicalIF":0.5000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":"{\"title\":\"Some properties of principal submodules in the module of entire functions of exponential type and polynomial growth on the real axis\",\"authors\":\"N. Abuzyarova\",\"doi\":\"10.13108/2016-8-1-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the work we consider a topological module of entire functions P(a; b), which is the isomorphic image of Fourier-Laplace transform of Schwarz space formed by distributions with compact supports in a finite or infinite segment (a; b) ⊂ R. We study the conditions ensuring that the principal submodule of module P(a; b) can be uniquely recovered by the zeroes of a generating function.\",\"PeriodicalId\":43644,\"journal\":{\"name\":\"Ufa Mathematical Journal\",\"volume\":\"34 1\",\"pages\":\"3-12\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2016-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ufa Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.13108/2016-8-1-1\",\"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":"Ufa Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13108/2016-8-1-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Some properties of principal submodules in the module of entire functions of exponential type and polynomial growth on the real axis
In the work we consider a topological module of entire functions P(a; b), which is the isomorphic image of Fourier-Laplace transform of Schwarz space formed by distributions with compact supports in a finite or infinite segment (a; b) ⊂ R. We study the conditions ensuring that the principal submodule of module P(a; b) can be uniquely recovered by the zeroes of a generating function.
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