对称加性测度的谱性

IF 0.8 4区数学 Q2 MATHEMATICS

Comptes Rendus Mathematique Pub Date : 2023-05-11 DOI:10.5802/crmath.435

Wen-Hui Ai, Zheng-Yi Lu, Ting Zhou

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引用次数: 0

摘要

其中分量测度μ是在[t,t+1]上支持的勒贝格测度，对于t∈π {-1 2}， δ 0是0处的狄拉克测度。我们证明ρ是一个谱测度当且仅当t∈1 2n。在这种情况下，l2 (ρ)有一个唯一的标准正交基的形式

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The spectrality of symmetric additive measures

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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来源期刊

Comptes Rendus Mathematique 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

115

审稿时长

16.6 weeks

期刊介绍： 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.