希尔伯特空间中的基

Control of Wave and Beam PDEs Pub Date : 2012-12-20 DOI:10.1155/2012/923729

Xunxiang Guo

{"title":"希尔伯特空间中的基","authors":"Xunxiang Guo","doi":"10.1155/2012/923729","DOIUrl":null,"url":null,"abstract":"The concept of g-basis in Hilbert spaces is introduced, which generalizes Schauder basis in Hilbert spaces. Some results about g-bases are proved. In particular, we characterize the g-bases and g-orthonormal bases. And the dual g-bases are also discussed. We also consider the equivalent relations of g-bases and g-orthonormal bases. And the property of g-minimal of g-bases is studied as well. Our results show that, in some cases, g-bases share many useful properties of Schauder bases in Hilbert spaces.","PeriodicalId":187086,"journal":{"name":"Control of Wave and Beam PDEs","volume":"2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Bases in Hilbert Spaces\",\"authors\":\"Xunxiang Guo\",\"doi\":\"10.1155/2012/923729\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The concept of g-basis in Hilbert spaces is introduced, which generalizes Schauder basis in Hilbert spaces. Some results about g-bases are proved. In particular, we characterize the g-bases and g-orthonormal bases. And the dual g-bases are also discussed. We also consider the equivalent relations of g-bases and g-orthonormal bases. And the property of g-minimal of g-bases is studied as well. Our results show that, in some cases, g-bases share many useful properties of Schauder bases in Hilbert spaces.\",\"PeriodicalId\":187086,\"journal\":{\"name\":\"Control of Wave and Beam PDEs\",\"volume\":\"2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-12-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Control of Wave and Beam PDEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2012/923729\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Control of Wave and Beam PDEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2012/923729","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 7

摘要

引入了Hilbert空间中g基的概念，推广了Hilbert空间中的Schauder基。证明了g基的一些结果。特别地，我们描述了g基和g标准正交基。并对双g基进行了讨论。我们还考虑了g基与g标准正交基的等价关系。并研究了g基的g极小的性质。我们的结果表明，在某些情况下，g基在Hilbert空间中具有Schauder基的许多有用性质。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Bases in Hilbert Spaces

The concept of g-basis in Hilbert spaces is introduced, which generalizes Schauder basis in Hilbert spaces. Some results about g-bases are proved. In particular, we characterize the g-bases and g-orthonormal bases. And the dual g-bases are also discussed. We also consider the equivalent relations of g-bases and g-orthonormal bases. And the property of g-minimal of g-bases is studied as well. Our results show that, in some cases, g-bases share many useful properties of Schauder bases in Hilbert spaces.

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

Control of Wave and Beam PDEs

自引率

0.00%

发文量

期刊最新文献

Bases in Hilbert Spaces Riesz Basis Generation: Comparison Method Riesz Basis Generation: Green Function Approach Riesz Basis Generation: Dual-Basis Approach Stabilization of Coupled Systems Through Boundary Connection