Cantor boundary behavior of analytic functions
Publication in refereed journal

香港中文大學研究人員
替代計量分析
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其它資訊
摘要Let A(D) be the space of analytic functions on the open disk D and continuous on D. Let ∂D be the boundary of D, we are interested in the class of f∈A(D) such that the image f(∂D) is a curve that forms loops everywhere. This fractal behavior was first raised by Lundetal.(1998)[21] in the study of the Cauchy transform of the Hausdorff measure on the Sierpinski gasket. We formulate the property as the Cantor boundary behavior (CBB) and establish two sufficient conditions through the distribution of zeros of f' (z) and the mean growth rate of {pipe}f' (z) {pipe} near the boundary. For the specific cases we carry out a detailed investigation on the gap series and the complex Weierstrass functions; the CBB for the Cauchy transform on the Sierpinski gasket will appear elsewhere. © 2012 Elsevier Ltd.
著者Dong X.-H., Lau K.-S., Liu J.-C.
期刊名稱Advances in Mathematics
出版年份2013
月份1
日期5
卷號232
期次1
出版社Academic Press
出版地United States
頁次543 - 570
國際標準期刊號0001-8708
電子國際標準期刊號1090-2082
語言英式英語
關鍵詞Analyticity, Blaschke product, Boundary behavior, Cantor set, Conformal, Fractal, Growth rate, Lacunary series, Simply connected, Univalence, Weierstrass function, Zeros

上次更新時間 2021-24-02 於 01:30