{"title":"一类单变量和多变量周期函数的Kolmogorov宽度","authors":"É. M. Galeev","doi":"10.1070/IM1991V036N02ABEH002029","DOIUrl":null,"url":null,"abstract":"The order of Kolmogorov widths are determined for the class that is the intersection of classes of periodic functions of one variable of \"higher\" smoothness, in the space for , and estimates from above for \"low\" smoothness, and also the order of Kolmogorov widths is calculated for periodic functions of several variables in the space for . The estimate from below for reduces to the estimate from below of the width of a finite-dimensional set whose width is determined. Bibliography: 28 titles.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"210 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"22","resultStr":"{\"title\":\"KOLMOGOROV WIDTHS OF CLASSES OF PERIODIC FUNCTIONS OF ONE AND SEVERAL VARIABLES\",\"authors\":\"É. M. Galeev\",\"doi\":\"10.1070/IM1991V036N02ABEH002029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The order of Kolmogorov widths are determined for the class that is the intersection of classes of periodic functions of one variable of \\\"higher\\\" smoothness, in the space for , and estimates from above for \\\"low\\\" smoothness, and also the order of Kolmogorov widths is calculated for periodic functions of several variables in the space for . The estimate from below for reduces to the estimate from below of the width of a finite-dimensional set whose width is determined. Bibliography: 28 titles.\",\"PeriodicalId\":159459,\"journal\":{\"name\":\"Mathematics of The Ussr-izvestiya\",\"volume\":\"210 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1991-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"22\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-izvestiya\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/IM1991V036N02ABEH002029\",\"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-izvestiya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/IM1991V036N02ABEH002029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
KOLMOGOROV WIDTHS OF CLASSES OF PERIODIC FUNCTIONS OF ONE AND SEVERAL VARIABLES
The order of Kolmogorov widths are determined for the class that is the intersection of classes of periodic functions of one variable of "higher" smoothness, in the space for , and estimates from above for "low" smoothness, and also the order of Kolmogorov widths is calculated for periodic functions of several variables in the space for . The estimate from below for reduces to the estimate from below of the width of a finite-dimensional set whose width is determined. Bibliography: 28 titles.
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