{"title":"Absolute Continuity and Singularity of Spectra for the Flows \\(T_t\\otimes T_{at}\\)","authors":"V. V. Ryzhikov","doi":"10.1134/S0016266322030066","DOIUrl":null,"url":null,"abstract":"<p> Given disjoint countable dense subsets <span>\\(C\\)</span> and <span>\\(D\\)</span> of the half-line <span>\\((1,+\\infty)\\)</span>, there exists a flow <span>\\(T_t\\)</span> preserving a sigma-finite measure and such that all automorphisms <span>\\(T_1\\otimes T_{c}\\)</span> with <span>\\(c\\in C\\)</span> have simple singular spectrum and all automorphisms <span>\\(T_1\\otimes T_{d}\\)</span> with <span>\\(d\\in D\\)</span> have Lebesgue spectrum of countable multiplicity. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 3","pages":"225 - 228"},"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/S0016266322030066","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
Given disjoint countable dense subsets \(C\) and \(D\) of the half-line \((1,+\infty)\), there exists a flow \(T_t\) preserving a sigma-finite measure and such that all automorphisms \(T_1\otimes T_{c}\) with \(c\in C\) have simple singular spectrum and all automorphisms \(T_1\otimes T_{d}\) with \(d\in D\) have Lebesgue spectrum of countable multiplicity.
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.