{"title":"The spectrality of symmetric additive measures","authors":"Wen-Hui Ai, Zheng-Yi Lu, Ting Zhou","doi":"10.5802/crmath.435","DOIUrl":null,"url":null,"abstract":"where the component measure μ is the Lebesgue measure supported on [t,t+1] for t∈ℚ∖{-1 2} and δ 0 is the Dirac measure at 0. We prove that ρ is a spectral measure if and only if t∈1 2ℤ. In this case, L 2 (ρ) has a unique orthonormal basis of the form","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus Mathematique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/crmath.435","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
where the component measure μ is the Lebesgue measure supported on [t,t+1] for t∈ℚ∖{-1 2} and δ 0 is the Dirac measure at 0. We prove that ρ is a spectral measure if and only if t∈1 2ℤ. In this case, L 2 (ρ) has a unique orthonormal basis of the form
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The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, …
Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English.
The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.
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