{"title":"无限框架的共边界算子","authors":"E. Kastis, D. Kitson, S. Power","doi":"10.3318/pria.2019.119.07","DOIUrl":null,"url":null,"abstract":"We consider, from the point of view of operator theory, a class of infinite matrices in which the matrix entries are determined by an underlying graph structure with accompanying geometric data. This class includes the rigidity matrices of infinite bar-joint frameworks as well as the incidence matrices of infinite directed graphs. We consider the following questions: When do these matrices give rise to bounded operators? Can we compute the operator norm? When are these operators compact? And when are they bounded below?","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"38 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Coboundary operators for infinite frameworks\",\"authors\":\"E. Kastis, D. Kitson, S. Power\",\"doi\":\"10.3318/pria.2019.119.07\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider, from the point of view of operator theory, a class of infinite matrices in which the matrix entries are determined by an underlying graph structure with accompanying geometric data. This class includes the rigidity matrices of infinite bar-joint frameworks as well as the incidence matrices of infinite directed graphs. We consider the following questions: When do these matrices give rise to bounded operators? Can we compute the operator norm? When are these operators compact? And when are they bounded below?\",\"PeriodicalId\":434988,\"journal\":{\"name\":\"Mathematical Proceedings of the Royal Irish Academy\",\"volume\":\"38 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Proceedings of the Royal Irish Academy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3318/pria.2019.119.07\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Royal Irish Academy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3318/pria.2019.119.07","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We consider, from the point of view of operator theory, a class of infinite matrices in which the matrix entries are determined by an underlying graph structure with accompanying geometric data. This class includes the rigidity matrices of infinite bar-joint frameworks as well as the incidence matrices of infinite directed graphs. We consider the following questions: When do these matrices give rise to bounded operators? Can we compute the operator norm? When are these operators compact? And when are they bounded below?
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