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.
{"title":"Bases in Hilbert Spaces","authors":"Xunxiang Guo","doi":"10.1155/2012/923729","DOIUrl":"https://doi.org/10.1155/2012/923729","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":0.0,"publicationDate":"2012-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123950219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-3-030-12481-6_5
B. Guo, Jun‐min Wang
{"title":"Riesz Basis Generation: Green Function Approach","authors":"B. Guo, Jun‐min Wang","doi":"10.1007/978-3-030-12481-6_5","DOIUrl":"https://doi.org/10.1007/978-3-030-12481-6_5","url":null,"abstract":"","PeriodicalId":187086,"journal":{"name":"Control of Wave and Beam PDEs","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121393986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-3-030-12481-6_6
B. Guo, Jun‐min Wang
{"title":"Stabilization of Coupled Systems Through Boundary Connection","authors":"B. Guo, Jun‐min Wang","doi":"10.1007/978-3-030-12481-6_6","DOIUrl":"https://doi.org/10.1007/978-3-030-12481-6_6","url":null,"abstract":"","PeriodicalId":187086,"journal":{"name":"Control of Wave and Beam PDEs","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130144851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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