{"title":"关于支持定理","authors":"S. Tôgô","doi":"10.32917/hmj/1206139313","DOIUrl":null,"url":null,"abstract":"We denote by ^ _ i the 7z—1 dimensional space consisting of elements ξ'. Let 2), S? and 0 M be the spaces of all C°°-functions with compact supports, all rapidly decreasing C°°-functions and all slowly increasing C°°-functions on Rn respectively. These spaces are provided with usual topologies of L. Schwartz \\JΓ\\. Let 2X and έf be the strong duals of 2) and Sf respectively and let O'c be the space of all rapidly decreasing distributions. We shall denote by Quiβn-x) the space 0M considered on Ξn-i. By the partial Fourier transform of T e Sf' we understand the Fourier transform of T with respect to the first n—1 variables which will be denoted by t(ξ\\ t). For any A(ξ') e O M ( ^ _ I ) , we define the operator A(DX,) on y\" as follows: The partial Fourier transform of A(DX,) T, Γ e / , is A(ξ') f(ξ\\ t). In this paper we are concerned with the operator of the following form :","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"22 1","pages":"43-49"},"PeriodicalIF":0.0000,"publicationDate":"1965-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On support theorems\",\"authors\":\"S. Tôgô\",\"doi\":\"10.32917/hmj/1206139313\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We denote by ^ _ i the 7z—1 dimensional space consisting of elements ξ'. Let 2), S? and 0 M be the spaces of all C°°-functions with compact supports, all rapidly decreasing C°°-functions and all slowly increasing C°°-functions on Rn respectively. These spaces are provided with usual topologies of L. Schwartz \\\\JΓ\\\\. Let 2X and έf be the strong duals of 2) and Sf respectively and let O'c be the space of all rapidly decreasing distributions. We shall denote by Quiβn-x) the space 0M considered on Ξn-i. By the partial Fourier transform of T e Sf' we understand the Fourier transform of T with respect to the first n—1 variables which will be denoted by t(ξ\\\\ t). For any A(ξ') e O M ( ^ _ I ) , we define the operator A(DX,) on y\\\" as follows: The partial Fourier transform of A(DX,) T, Γ e / , is A(ξ') f(ξ\\\\ t). In this paper we are concerned with the operator of the following form :\",\"PeriodicalId\":17080,\"journal\":{\"name\":\"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry\",\"volume\":\"22 1\",\"pages\":\"43-49\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1965-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32917/hmj/1206139313\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32917/hmj/1206139313","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
我们用^ i表示由元素ξ'组成的7z-1维空间。设2)S?和0 M分别为Rn上所有具有紧支承的C°°-函数、所有速降C°°-函数和所有慢增C°°-函数的空间。这些空间由L. Schwartz \JΓ\的常用拓扑提供。设2X和f分别是2)和Sf的强对偶设O'c是所有速降分布的空间。我们将用q βn-x表示在Ξn-i上考虑的空间0M。通过T的傅里叶偏变换,我们可以理解T对前n-1个变量的傅里叶变换,这些变量记为T (ξ\ T).对于任意A(ξ′)e O M (^ _ I),我们定义y′上的算子A(DX,)如下:A(DX,) T, Γ e /的傅里叶偏变换为A(ξ′)f(ξ\ T).本文讨论的算子的形式如下:
We denote by ^ _ i the 7z—1 dimensional space consisting of elements ξ'. Let 2), S? and 0 M be the spaces of all C°°-functions with compact supports, all rapidly decreasing C°°-functions and all slowly increasing C°°-functions on Rn respectively. These spaces are provided with usual topologies of L. Schwartz \JΓ\. Let 2X and έf be the strong duals of 2) and Sf respectively and let O'c be the space of all rapidly decreasing distributions. We shall denote by Quiβn-x) the space 0M considered on Ξn-i. By the partial Fourier transform of T e Sf' we understand the Fourier transform of T with respect to the first n—1 variables which will be denoted by t(ξ\ t). For any A(ξ') e O M ( ^ _ I ) , we define the operator A(DX,) on y" as follows: The partial Fourier transform of A(DX,) T, Γ e / , is A(ξ') f(ξ\ t). In this paper we are concerned with the operator of the following form :