论流形 $$\mathbb R^n\times\mathbb T^m$$ 上一族算子的最佳恢复力

Pub Date : 2024-03-06 DOI:10.1134/s0081543823050115

G. G. Magaril-Il’yaev, E. O. Sivkova

{"title":"论流形 $$\\mathbb R^n\\times\\mathbb T^m$$ 上一族算子的最佳恢复力","authors":"G. G. Magaril-Il’yaev, E. O. Sivkova","doi":"10.1134/s0081543823050115","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Given a one-parameter family of operators on the manifold <span>\$\\mathbb R^n\\times\\mathbb T^m\$</span>, we solve the problem of the best recovery of an operator for a given value of the parameter from inaccurate data on the operators for other values of the parameter from a certain compact set. We construct a family of best recovery methods. As a consequence, we obtain families of best recovery methods for the solutions of the heat equation and the Dirichlet problem for a half-space. </p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Best Recovery of a Family of Operators on the Manifold $$\\\\mathbb R^n\\\\times\\\\mathbb T^m$$\",\"authors\":\"G. G. Magaril-Il’yaev, E. O. Sivkova\",\"doi\":\"10.1134/s0081543823050115\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> Given a one-parameter family of operators on the manifold <span>\\\$\\\\mathbb R^n\\\\times\\\\mathbb T^m\\\$</span>, we solve the problem of the best recovery of an operator for a given value of the parameter from inaccurate data on the operators for other values of the parameter from a certain compact set. We construct a family of best recovery methods. As a consequence, we obtain families of best recovery methods for the solutions of the heat equation and the Dirichlet problem for a half-space. </p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-03-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0081543823050115\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0081543823050115","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

Abstract Given a one-parameter family of operators on the manifold $\mathbb R^n\times\mathbb T^m$， we solve the problem of the best recovery of an operator for a given value of the parameter from inaccurate data on the operators for other values of the parameter from a certain compact set.我们构建了一个最佳复原方法族。因此，我们得到了半空间热方程和迪里夏特问题解的最佳复原方法族。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

On the Best Recovery of a Family of Operators on the Manifold $$\mathbb R^n\times\mathbb T^m$$

Abstract

Given a one-parameter family of operators on the manifold $\mathbb R^n\times\mathbb T^m$, we solve the problem of the best recovery of an operator for a given value of the parameter from inaccurate data on the operators for other values of the parameter from a certain compact set. We construct a family of best recovery methods. As a consequence, we obtain families of best recovery methods for the solutions of the heat equation and the Dirichlet problem for a half-space.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助