{"title":"Cyclic Vectors and Invariant Subspaces of the Backward Shift Operator in Schwartz Modules","authors":"O. A. Ivanova, S. N. Melikhov","doi":"10.1134/S0016266322030030","DOIUrl":null,"url":null,"abstract":"<p> Cyclic vectors and proper closed invariant subspaces of the backward shift operator in the Schwartz modules of entire functions of exponential type are described. The results are applied to describe ideals of the algebra of infinitely differentiable functions on a closed or open interval containing <span>\\(0\\)</span> with Duhamel product as multiplication. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Functional Analysis and Its Applications","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S0016266322030030","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Cyclic vectors and proper closed invariant subspaces of the backward shift operator in the Schwartz modules of entire functions of exponential type are described. The results are applied to describe ideals of the algebra of infinitely differentiable functions on a closed or open interval containing \(0\) with Duhamel product as multiplication.
期刊介绍：
Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
