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Estimates for Taylor coefficients of Cauchy transforms of some Hausdorff Measures (II)
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2020-05-25 , DOI: 10.1016/j.jfa.2020.108654
Hong-Guang Li , Xin-Han Dong , Peng-Fei Zhang

Let q be even, F be the Cauchy transform of the self-similar measure μ=1qj=0q1μSj where Sj(z)=e2jπi/q+ρ(ze2jπi/q) with ρ(0,1), and K be the attractor of {Sj}j=0q1 and Rq=dist(0,K). As a follow-up of [8], we not only study the asymptotic formula for the Taylor coefficients {bqk1}k=1 of F in |z|<Rq, but also the chaotic behavior of F(n) near the attractor K.



中文翻译:

一些Hausdorff测度的柯西变换的泰勒系数估计(II)

q为偶数,F为自相似度量的柯西变换μ=1个qĴ=0q-1个μ小号Ĵ 哪里 小号Ĵž=Ë2Ĵπ一世/q+ρž-Ë2Ĵπ一世/qρ01个,并且K是...的吸引子{小号Ĵ}Ĵ=0q-1个[Rq=dist0ķ。作为[8]的后续,我们不仅研究泰勒系数的渐近公式{bqķ-1个}ķ=1个F in|ž|<[Rq,而且还有 Fñ在吸引子K附近。

更新日期:2020-05-25
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