{"title":"具有无穷维解空间的序列系数线性差分算子","authors":"S. Abramov, G. Pogudin","doi":"10.1145/3610377.3610378","DOIUrl":null,"url":null,"abstract":"The notion of lacunary infinite numerical sequence is introduced. It is shown that for an arbitrary linear difference operator L with coefficients belonging to the set R of infinite numerical sequences, a criterion (i.e., a necessary and sufficient condition) for the infinite-dimensionality of its space VL of solutions belonging to R is the presence of a lacunary sequence in VL.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"57 1","pages":"1 - 4"},"PeriodicalIF":0.4000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linear Difference Operators with Sequence Coefficients Having Infinite-Dimentional Solution Spaces\",\"authors\":\"S. Abramov, G. Pogudin\",\"doi\":\"10.1145/3610377.3610378\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The notion of lacunary infinite numerical sequence is introduced. It is shown that for an arbitrary linear difference operator L with coefficients belonging to the set R of infinite numerical sequences, a criterion (i.e., a necessary and sufficient condition) for the infinite-dimensionality of its space VL of solutions belonging to R is the presence of a lacunary sequence in VL.\",\"PeriodicalId\":41965,\"journal\":{\"name\":\"ACM Communications in Computer Algebra\",\"volume\":\"57 1\",\"pages\":\"1 - 4\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Communications in Computer Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3610377.3610378\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Communications in Computer Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3610377.3610378","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Linear Difference Operators with Sequence Coefficients Having Infinite-Dimentional Solution Spaces
The notion of lacunary infinite numerical sequence is introduced. It is shown that for an arbitrary linear difference operator L with coefficients belonging to the set R of infinite numerical sequences, a criterion (i.e., a necessary and sufficient condition) for the infinite-dimensionality of its space VL of solutions belonging to R is the presence of a lacunary sequence in VL.
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