Generalization of results about the Bohr radius for power series

By L. Aĭzenberg. 2006

86 citations recorded by the source corpus.

The Bohr radius for power series of holomorphic functions mapping a multidimensional Reinhardt domain into the convex domain in the complex plane is independent of this convex domain.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a43469328c677ab5787c4642a58f4707668f723d

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In Applied Mathematics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Bohr--Rogosinski radius for analytic functions (2017, background): “The notion of Bohr’s radius, initially defined for analytic functions from the unit disk D into D, was generalized by authors to include mappings from D to some other domains Ω in D ( [1,2,4]).”
A note on Bohr's phenomenon for power series (2017, background): “The notion of Bohr’s radius, initially defined for mappings from the unit disk D to itself, was generalized by some authors to classes of mappings from D to some other domains G ⊂ C (see [7,1,3,5]).”
Bohr Radius for Subordination and K-quasiconformal Harmonic Mappings (2019, background): “(g) For α ∈ [1, 2], the function φ(z) = 1 2α [( 1 + z 1− z )α − 1 ]”
Sharp Bohr type inequality (2020, background): “It is worth pointing out that the notion of Bohr’s radius, initially defined for analytic functions from the unit disk D into D, was generalized by authors to include mappings from D to some other domains Ω in D ( [1, 2, 5]).”
Bohr radius for certain classes of starlike and convex univalent functions (2020, background): “ (see [37, 44, 47]). The inequality (1.2) is popularly known as Bohr’s inequality. The Bohr’s inequality has been extended to several complex variables by ﬁnding the multidimensional Bohr radius (see [5, 6, 7, 14, 15]). File: Himadri-Vasu-27-june-2020-1.20-a.m..tex, printed: 2020-6-30, 0.52 1991 Mat”
On the Bohr inequality with a fixed zero coefficient (2019, background): “In particular, Boas and Khavinson [8], Aizenberg [2, 3], and Aizenberg and Tarkhanov [4] have extended the Bohr inequality for holomorphic functions on certain specific domains (such as complete Reinhardt domain) in C.”
Multidimensional analogues of refined Bohr’s inequality (2020, unknown): “For example, Aizenberg [1, 2, 3], Aizenberg et al.”
Bohr phenomenon for certain subclasses of harmonic mappings (2020, background): “ius rG > 0 such that (1.5) X∞ n=1 |anz n| ≤ d(f(0),∂f(D)) in |z| < r G for all functions f belong to the class of analytic functions in Dsuch that f(D) ⊆ G. For a convex domain G ⊆ D, Aizenberg [7] has obtained the largest radius rG, for which the inequality (1.5) holds, coincides with the cla”
The Bohr radius for starlike logharmonic mappings (2016, unknown): “[11] Aizenberg L, Tarkhanov N.”
Bohr radius for subordinating families of analytic functions and bounded harmonic mappings (2014, result): “This result established a link between the results of Aizenberg [5] and Abu-Muhanna [1].”
Bohr’s theorem for holomorphic mappings with values in homogeneous balls (2009, unknown): “tion of Bohr’s theorem to several complex variables, see [2], [ 3 ], [4], [5], [9], [10], [11], [14], [19], [20] and [21].”