Cauchy transforms of self-similar measures: Starlikeness and univalence
نویسندگان
چکیده
منابع مشابه
Cauchy Transforms of Self-Similar Measures
is a useful tool for numerical studies of the measure, since the measure of any reasonable set may be obtained as the line integral of F around the boundary. We give an effective algorithm for computing F when is a self-similar measure, based on a Laurent expansion of F for large z and a transformation law (Theorem 2.2) for F that encodes the self-similarity of . Using this algorithm we compute...
متن کاملCauchy transforms of self-similar measures: the Laurent coefficients
The Cauchy transform of a measure has been used to study the analytic capacity and uniform rectifiability of subsets in C: Recently, Lund et al. (Experiment. Math. 7 (1998) 177) have initiated the study of such transform F of self-similar measure. In this and the forecoming papers (Starlikeness and the Cauchy transform of some self-similar measures, in preparation; The Cauchy transform on the S...
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It is known that the condition $mathfrak {Re} left{zf'(z)/f(z)right}>0$, $|z|
متن کاملSome Sufficient Conditions for Univalence and Starlikeness
The object of the present paper is to derive certain sufficient conditions for univalence, p-valently starlikeness and p-valently close-to-convexity of analytic functions in the unit disk. Our results extend and improve some results due to Owa [3], Frasin and Darus [2] and Chen [1].
متن کاملLarge Scale Renormalisation of Fourier Transforms of Self-similar Measures and Self-similarity of Riesz Measures
We shall show that the oscillations observed by Strichartz JRS92, Str90] in the Fourier transforms of self-similar measures have a large-scale renormali-sation given by a Riesz-measure. Vice versa the Riesz measure itself will be shown to be self-similar around every triadic point.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2016
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6819