齐次自仿射测度的傅立叶衰减

IF 1.1 4区数学 Q1 MATHEMATICS

Journal of Fractal Geometry Pub Date : 2021-05-17 DOI:10.4171/jfg/119

B. Solomyak

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引用次数: 6

摘要

lim pμpξq“0，如|ξ|ñ8，其中|ξ|r是ξp Rd的范数（比如欧几里得范数）。虽然绝对连续测度是Riemann-Lebesgue引理的Rajchman，但决定哪些奇异测度是这样的是一个微妙的问题，例如参见Lyons的调查[14]。一个更强的性质，对许多应用都有用，如下定义1.1。设Ddpαq“ΓRd上的有限正测度：|pΓptq|”OΓp|t|q，|t|ñ8(

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Fourier decay for homogeneous self-affine measures

lim p μpξq “ 0, as |ξ| Ñ 8, where |ξ| is a norm (say, the Euclidean norm) of ξ P Rd. Whereas absolutely continuous measures are Rajchman by the Riemann-Lebesgue Lemma, it is a subtle question to decide which singular measures are such, see, e.g., the survey of Lyons [14]. A much stronger property, useful for many applications is the following. Definition 1.1. For α ą 0 let Ddpαq “ ν finite positive measure on Rd : |p νptq| “ Oνp|t|q, |t| Ñ 8 (

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来源期刊

Journal of Fractal Geometry MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量