闭算子解级数的反演及其应用

Siberian Advances in Mathematics Pub Date : 2022-06-18 DOI:10.1134/s1055134422020079

A. R. Mirotin

{"title":"闭算子解级数的反演及其应用","authors":"A. R. Mirotin","doi":"10.1134/s1055134422020079","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider an operator represented by the sum of a series in the values of the resolvent of\na densely defined closed operator in a complex Banach space. We describe the left inverse for this\noperator, apply this result to regularization of equations of the first kind, and consider several\nexamples.\n</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"47 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inversion of Series of Resolvents for Closed Operators and Some Applications\",\"authors\":\"A. R. Mirotin\",\"doi\":\"10.1134/s1055134422020079\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> We consider an operator represented by the sum of a series in the values of the resolvent of\\na densely defined closed operator in a complex Banach space. We describe the left inverse for this\\noperator, apply this result to regularization of equations of the first kind, and consider several\\nexamples.\\n</p>\",\"PeriodicalId\":39997,\"journal\":{\"name\":\"Siberian Advances in Mathematics\",\"volume\":\"47 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Siberian Advances in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1055134422020079\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Advances in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1055134422020079","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

考虑复Banach空间中稠密定义闭算子的解值的级数和所表示的算子。我们描述了这个算子的左逆，将这个结果应用于第一类方程的正则化，并考虑了几个例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Inversion of Series of Resolvents for Closed Operators and Some Applications

Abstract

We consider an operator represented by the sum of a series in the values of the resolvent of a densely defined closed operator in a complex Banach space. We describe the left inverse for this operator, apply this result to regularization of equations of the first kind, and consider several examples.

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

来源期刊

Siberian Advances in Mathematics Mathematics-Mathematics (all)

CiteScore

0.70

自引率

0.00%

发文量

期刊介绍： Siberian Advances in Mathematics is a journal that publishes articles on fundamental and applied mathematics. It covers a broad spectrum of subjects: algebra and logic, real and complex analysis, functional analysis, differential equations, mathematical physics, geometry and topology, probability and mathematical statistics, mathematical cybernetics, mathematical economics, mathematical problems of geophysics and tomography, numerical methods, and optimization theory.