{"title":"局部凸空间中常线性微分方程可解性的一些结果","authors":"S. Shkarin","doi":"10.1070/SM1992v071n01ABEH002126","DOIUrl":null,"url":null,"abstract":"Let be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem , , with respect to functions . It is proved that if , then for an arbitrary set . It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to , does not belong to .","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"45-46 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":"{\"title\":\"SOME RESULTS ON SOLVABILITY OF ORDINARY LINEAR DIFFERENTIAL EQUATIONS IN LOCALLY CONVEX SPACES\",\"authors\":\"S. Shkarin\",\"doi\":\"10.1070/SM1992v071n01ABEH002126\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem , , with respect to functions . It is proved that if , then for an arbitrary set . It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to , does not belong to .\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"45-46 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"16\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1992v071n01ABEH002126\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992v071n01ABEH002126","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
SOME RESULTS ON SOLVABILITY OF ORDINARY LINEAR DIFFERENTIAL EQUATIONS IN LOCALLY CONVEX SPACES
Let be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem , , with respect to functions . It is proved that if , then for an arbitrary set . It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to , does not belong to .
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