{"title":"空间 $B_{q,1}$ 中一变量和多变量周期函数类的宽度和熵数","authors":"K. Pozharska, A. S. Romanyuk, V. Romanyuk","doi":"10.15330/cmp.16.2.351-366","DOIUrl":null,"url":null,"abstract":"Exact-order estimates are obtained for the entropy numbers and several types of widths (Kolmogorov, linear, trigonometric and orthowidth) for the Sobolev and Nikol'skii-Besov classes of one and several variables in the space $B_{q,1}$, $1 <q< \\infty$. It is shown, that in the multivariate case, in contrast to the univariate, the obtained estimates differ in order from the corresponding estimates in the space $L_q$.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Widths and entropy numbers of the classes of periodic functions of one and several variables in the space $B_{q,1}$\",\"authors\":\"K. Pozharska, A. S. Romanyuk, V. Romanyuk\",\"doi\":\"10.15330/cmp.16.2.351-366\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Exact-order estimates are obtained for the entropy numbers and several types of widths (Kolmogorov, linear, trigonometric and orthowidth) for the Sobolev and Nikol'skii-Besov classes of one and several variables in the space $B_{q,1}$, $1 <q< \\\\infty$. It is shown, that in the multivariate case, in contrast to the univariate, the obtained estimates differ in order from the corresponding estimates in the space $L_q$.\",\"PeriodicalId\":42912,\"journal\":{\"name\":\"Carpathian Mathematical Publications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-07-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Carpathian Mathematical Publications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15330/cmp.16.2.351-366\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Carpathian Mathematical Publications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15330/cmp.16.2.351-366","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Widths and entropy numbers of the classes of periodic functions of one and several variables in the space $B_{q,1}$
Exact-order estimates are obtained for the entropy numbers and several types of widths (Kolmogorov, linear, trigonometric and orthowidth) for the Sobolev and Nikol'skii-Besov classes of one and several variables in the space $B_{q,1}$, $1