Infinite Dimensional Widths and Optimal Recovery of a Function Class in Orlicz Spaces in L(R) Metric
In this paper, we study the infinite dimensional widths and optimal recovery of Wiener–Sobolev smooth function classes WM,1(Pr(D)) determined by the r-th differential operator Pr(D) in Orlicz spaces with L(R) metric. Using tools such as the Hölder inequality, we give the exact values of the infinite...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/6616280 |
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| author | Xinxin Li Garidi Wu |
| author_facet | Xinxin Li Garidi Wu |
| author_sort | Xinxin Li |
| collection | DOAJ |
| description | In this paper, we study the infinite dimensional widths and optimal recovery of Wiener–Sobolev smooth function classes WM,1(Pr(D)) determined by the r-th differential operator Pr(D) in Orlicz spaces with L(R) metric. Using tools such as the Hölder inequality, we give the exact values of the infinite dimensional Kolmogorov width and linear width of WM,1(Pr(D)) in L(R) metric. We also study the related optimal recovery problem. |
| format | Article |
| id | doaj-art-80ec10307ccf4730baf0bcfd0984c9b5 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-80ec10307ccf4730baf0bcfd0984c9b52025-08-20T02:08:53ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/6616280Infinite Dimensional Widths and Optimal Recovery of a Function Class in Orlicz Spaces in L(R) MetricXinxin Li0Garidi Wu1College of Mathematics ScienceCollege of Mathematics ScienceIn this paper, we study the infinite dimensional widths and optimal recovery of Wiener–Sobolev smooth function classes WM,1(Pr(D)) determined by the r-th differential operator Pr(D) in Orlicz spaces with L(R) metric. Using tools such as the Hölder inequality, we give the exact values of the infinite dimensional Kolmogorov width and linear width of WM,1(Pr(D)) in L(R) metric. We also study the related optimal recovery problem.http://dx.doi.org/10.1155/2023/6616280 |
| spellingShingle | Xinxin Li Garidi Wu Infinite Dimensional Widths and Optimal Recovery of a Function Class in Orlicz Spaces in L(R) Metric Journal of Mathematics |
| title | Infinite Dimensional Widths and Optimal Recovery of a Function Class in Orlicz Spaces in L(R) Metric |
| title_full | Infinite Dimensional Widths and Optimal Recovery of a Function Class in Orlicz Spaces in L(R) Metric |
| title_fullStr | Infinite Dimensional Widths and Optimal Recovery of a Function Class in Orlicz Spaces in L(R) Metric |
| title_full_unstemmed | Infinite Dimensional Widths and Optimal Recovery of a Function Class in Orlicz Spaces in L(R) Metric |
| title_short | Infinite Dimensional Widths and Optimal Recovery of a Function Class in Orlicz Spaces in L(R) Metric |
| title_sort | infinite dimensional widths and optimal recovery of a function class in orlicz spaces in l r metric |
| url | http://dx.doi.org/10.1155/2023/6616280 |
| work_keys_str_mv | AT xinxinli infinitedimensionalwidthsandoptimalrecoveryofafunctionclassinorliczspacesinlrmetric AT garidiwu infinitedimensionalwidthsandoptimalrecoveryofafunctionclassinorliczspacesinlrmetric |