对称加性测度的谱性

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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