{"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}
引用次数: 0
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.
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