{"title":"重现核希尔伯特空间不能包含紧凑公元空间上的所有连续函数","authors":"Ingo Steinwart","doi":"10.1007/s00013-024-01976-0","DOIUrl":null,"url":null,"abstract":"<div><p>Given an uncountable, compact metric space <i>X</i>, we show that there exists no reproducing kernel Hilbert space that contains the space of all continuous functions on <i>X</i>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-01976-0.pdf","citationCount":"0","resultStr":"{\"title\":\"Reproducing kernel Hilbert spaces cannot contain all continuous functions on a compact metric space\",\"authors\":\"Ingo Steinwart\",\"doi\":\"10.1007/s00013-024-01976-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Given an uncountable, compact metric space <i>X</i>, we show that there exists no reproducing kernel Hilbert space that contains the space of all continuous functions on <i>X</i>.</p></div>\",\"PeriodicalId\":8346,\"journal\":{\"name\":\"Archiv der Mathematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-03-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00013-024-01976-0.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archiv der Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00013-024-01976-0\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00013-024-01976-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Reproducing kernel Hilbert spaces cannot contain all continuous functions on a compact metric space
Given an uncountable, compact metric space X, we show that there exists no reproducing kernel Hilbert space that contains the space of all continuous functions on X.
期刊介绍：
Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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