Bohr Phenomenon for Locally Univalent Functions and Logarithmic Power Series
نویسندگان
چکیده
منابع مشابه
Univalent functions of fast growth with gap power series
We construct univalent functions in the unit disc, whose coefficient sequences (an) have arbitrarily long intervals of zeros, and at the same time arbitrarily long intervals where |an| > n n holds, ( n) being an an arbitrary prescribed sequence of positive numbers tending to zero. Furthermore we show that the initial interval of coefficients of such a function can be prescribed to be any interi...
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Bohr’s theorem ([10]) states that analytic functions bounded by 1 in the unit disk have power series ∑ anz n such that ∑ |an||z| < 1 in the disk of radius 1/3 (the so-called Bohr radius.) On the other hand, it is known that there is no such Bohr phenomenon in Hardy spaces with the usual norm, although it is possible to build equivalent norms for which a Bohr phenomenon does occur! In this paper...
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ژورنال
عنوان ژورنال: Computational Methods and Function Theory
سال: 2019
ISSN: 1617-9447,2195-3724
DOI: 10.1007/s40315-019-00291-y