{"title":"关于Muntz-Szasz型定理的注解","authors":"Morisuke Hasumi","doi":"10.5036/BFSIU1968.15.19","DOIUrl":null,"url":null,"abstract":"function on the interval [0, 1] with φ(0)=0 and let {n(k):k=1,2,...} be a strictly increasing sequence of positive real numbers tending to infinity. Then we have the following: (a) Let C0[0, 1] be the space of (real-or complex-valued) continuous functions on [0, 1] vanishing at 0, equipped with the usual uniform norm. Then, the system {φn(k):k=1,2,...} is fundamental in C0[0, 1] if and only if Σ ∞k=1η(k)-1=","PeriodicalId":141145,"journal":{"name":"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics","volume":"95 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1983-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Remarks on Theorems of Muntz-Szasz Type\",\"authors\":\"Morisuke Hasumi\",\"doi\":\"10.5036/BFSIU1968.15.19\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"function on the interval [0, 1] with φ(0)=0 and let {n(k):k=1,2,...} be a strictly increasing sequence of positive real numbers tending to infinity. Then we have the following: (a) Let C0[0, 1] be the space of (real-or complex-valued) continuous functions on [0, 1] vanishing at 0, equipped with the usual uniform norm. Then, the system {φn(k):k=1,2,...} is fundamental in C0[0, 1] if and only if Σ ∞k=1η(k)-1=\",\"PeriodicalId\":141145,\"journal\":{\"name\":\"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics\",\"volume\":\"95 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1983-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5036/BFSIU1968.15.19\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5036/BFSIU1968.15.19","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
function on the interval [0, 1] with φ(0)=0 and let {n(k):k=1,2,...} be a strictly increasing sequence of positive real numbers tending to infinity. Then we have the following: (a) Let C0[0, 1] be the space of (real-or complex-valued) continuous functions on [0, 1] vanishing at 0, equipped with the usual uniform norm. Then, the system {φn(k):k=1,2,...} is fundamental in C0[0, 1] if and only if Σ ∞k=1η(k)-1=
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