{"title":"混合平滑函数的采样恢复","authors":"E. D. Kosov, V. N. Temlyakov","doi":"10.1007/s43036-025-00439-9","DOIUrl":null,"url":null,"abstract":"<div><p>Recently, a substantial progress in studying the problem of optimal sampling recovery was made in a number of papers. In particular, this resulted in some progress in studying sampling recovery on function classes with mixed smoothness. Mostly, the case of recovery in the square norm was studied. In this paper we combine some of the new ideas developed recently in order to obtain progress in sampling recovery on classes with mixed smoothness in other integral norms.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sampling recovery of functions with mixed smoothness\",\"authors\":\"E. D. Kosov, V. N. Temlyakov\",\"doi\":\"10.1007/s43036-025-00439-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Recently, a substantial progress in studying the problem of optimal sampling recovery was made in a number of papers. In particular, this resulted in some progress in studying sampling recovery on function classes with mixed smoothness. Mostly, the case of recovery in the square norm was studied. In this paper we combine some of the new ideas developed recently in order to obtain progress in sampling recovery on classes with mixed smoothness in other integral norms.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"10 2\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-04-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-025-00439-9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-025-00439-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Sampling recovery of functions with mixed smoothness
Recently, a substantial progress in studying the problem of optimal sampling recovery was made in a number of papers. In particular, this resulted in some progress in studying sampling recovery on function classes with mixed smoothness. Mostly, the case of recovery in the square norm was studied. In this paper we combine some of the new ideas developed recently in order to obtain progress in sampling recovery on classes with mixed smoothness in other integral norms.
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