{"title":"调和函数类的最佳和最优恢复方法","authors":"K. Osipenko","doi":"10.1070/SM1992V073N01ABEH002537","DOIUrl":null,"url":null,"abstract":"The author considers problems of best recovery of a functional , , in the space of harmonic functions for or 2, in terms of the values of the functions and their derivatives at points of the interval . In the space the problem of constructing best quadrature formulas is solved. The existence of optimal quadrature formulas is proved, and, under certain conditions, the uniqueness of the optimal knots.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"BEST AND OPTIMAL RECOVERY METHODS FOR CLASSES OF HARMONIC FUNCTIONS\",\"authors\":\"K. Osipenko\",\"doi\":\"10.1070/SM1992V073N01ABEH002537\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The author considers problems of best recovery of a functional , , in the space of harmonic functions for or 2, in terms of the values of the functions and their derivatives at points of the interval . In the space the problem of constructing best quadrature formulas is solved. The existence of optimal quadrature formulas is proved, and, under certain conditions, the uniqueness of the optimal knots.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"16 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1992V073N01ABEH002537\",\"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-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992V073N01ABEH002537","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
BEST AND OPTIMAL RECOVERY METHODS FOR CLASSES OF HARMONIC FUNCTIONS
The author considers problems of best recovery of a functional , , in the space of harmonic functions for or 2, in terms of the values of the functions and their derivatives at points of the interval . In the space the problem of constructing best quadrature formulas is solved. The existence of optimal quadrature formulas is proved, and, under certain conditions, the uniqueness of the optimal knots.
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