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In this article, we determine sharp Bohr-type radii for certain complex integral operators defined on a set of bounded analytic functions in the unit disk.

Complex Variables · Mathematics 2020-08-04 Shankey Kumar , Swadesh Kumar Sahoo

In this paper, we study some improved and refined versions of the classical Bohr inequality applicable to the class $\mathcal{B}$, which consists of self-analytic mappings defined on the unit disk $\mathbb{D}$. First, we improve the Bohr…

Complex Variables · Mathematics 2024-02-27 Molla Basir Ahamed , Partha Pratim Roy

This paper is devoted to the investigation of multidimensional analogues of refined Bohr-type inequalities for bounded holomorphic mappings on the unit polydisc $\mathbb{D}^n$. We establish a sharp extension of the classical Bohr…

Complex Variables · Mathematics 2026-01-13 Molla Basir Ahamed , Sujoy Majumder , Nabadwip Sarkar

This paper is to characterize piecewise continuous almost periodic functions as the product of Bohr almost periodic functions and sequences. As an application, the result is used to discuss piecewise continuous almost periodic solutions of…

Classical Analysis and ODEs · Mathematics 2018-02-27 Liangping Qi , Rong Yuan

We say that a class $\mathcal{F}$ consisting of analytic functions $f(z)=\sum_{n=0}^{\infty} a_{n}z^{n}$ in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}: |z|<1\}$ satisfies a Bohr phenomenon if there exists $r_{f} \in (0,1)$ such that $$…

Complex Variables · Mathematics 2020-06-30 Vasudevarao Allu , Himadri Halder

The main purpose of this paper is to prove some density results of polynomials in Fock spaces of slice regular functions. The spaces can be of two different kinds since they are equipped with different inner products and contain different…

Complex Variables · Mathematics 2018-12-10 Kamal Diki , Sorin G. Gal , Irene Sabadini

Given a slice regular function $f:\Omega\subset\mathbb{H}\to \mathbb{H}$, with $\Omega\cap\mathbb{R}\neq \emptyset$, it is possible to lift it to a surface in the twistor space $\mathbb{CP}^{3}$ of $\mathbb{S}^4\simeq \mathbb{H}\cup…

Complex Variables · Mathematics 2017-10-17 Amedeo Altavilla

Bohr phenomenon for analytic functions $ f $ where $ f(z)=\sum_{n=0}^{\infty}a_nz^n $, first introduced by Harald Bohr in $ 1914 $, deals with finding the largest radius $ r_f $, $ 0<r_f<1 $, such that the inequality $…

Complex Variables · Mathematics 2021-04-07 Molla Basir Ahamed , Vasudevarao Allu

Denoting by $\mathbb{M}$ the complexification of the quaternionic algebra $\mathbb{H}$, we characterize the family of those $\mathbb{M}$-valued functions, defined on subsets of $\H$, whose values are actually quaternions, using an intrinsic…

Functional Analysis · Mathematics 2019-05-31 Florian-Horia Vasilescu

In this paper, we establish five new sharp versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing Schwarz function in place of the initial coefficients in the power series representations of the…

Complex Variables · Mathematics 2020-09-14 Yong Huang , Ming-Sheng Liu , Saminathan Ponnusamy

This paper introduces a unified framework for Bohr-type inequalities by incorporating multiple Schwarz functions into the majorant series for $K$-quasiconformal harmonic mappings in the unit disk $\mathbb{D} := \{z\in\mathbb{C} : |z| <…

Complex Variables · Mathematics 2025-10-02 Raju Biswas , Rajib Mandal

The celebrated 100-year old Phragmen-Lindelof principle is a far reaching extension of the maximum modulus theorem for holomorphic functions of one complex variable. In some recent papers there has been a resurgence of interest in…

Complex Variables · Mathematics 2022-09-07 G. Gentili , C. Stoppato , D. C. Struppa

In this paper, several Bohr-type inequalities are generalized to the form with two parameters for the bounded analytic function. Most of the results are sharp.

Complex Variables · Mathematics 2025-02-06 Wanqing Hou , Qihan Wang , Boyong Long

The Bohr compactification is a well known construction for (topological) groups and semigroups. Recently, this notion has been investigated for arbitrary structures in \cite{har_kun:bohr_discrete} where the Bohr compactification is defined,…

Functional Analysis · Mathematics 2025-03-12 Salvador Hernández

The main aim of this article is to establish a sharp improvement of the classical Bohr inequality for bounded holomorphic mappings in the polydisk $\mathbb{P}\Delta(0;1_n)$. We also prove two other sharp versions of the Bohr inequality in…

Complex Variables · Mathematics 2025-12-09 Molla Basir Ahamed , Sujoy Majumder , Nabadwip Sarkar , Ming-Sheng Liu

Recently, there has been a number of good deal of research on the Bohr's phenomenon in various setting including a refined formulation of his classical version of the inequality. Among them, in \cite{PaulPopeSingh-02-10} the authors…

Complex Variables · Mathematics 2020-06-12 Saminathan Ponnusamy , Karl-Joachim Wirths

Given two arbitrary almost periodic functions with associated Fourier exponents which are linearly independent over the rational numbers, we prove that the existence of a common open vertical strip $V$, where both functions assume the same…

Classical Analysis and ODEs · Mathematics 2021-05-04 M. Righetti , J. M. Sepulcre , T. Vidal

We introduce and study the algebraic, analytic and lattice properties of regular homogeneous polynomials and holomorphic functions on complex Banach lattices. We show that the theory of power series with regular terms is closer to the…

Functional Analysis · Mathematics 2024-06-28 Christopher Boyd , Raymond A. Ryan , Nina Snigireva

In this paper, we generalize and investigate Bohr-Rogosinski's inequalities and the Bohr-Rogosinski phenomenon for the subfamilies of univalent (i.e., one-to-one) functions defined on unit disk $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1 \}$ which…

Complex Variables · Mathematics 2022-05-02 Vasudevarao Allu , Vibhuti Arora

In this paper, we investigates the Bohr phenomenon for holomorphic mappings $F$ from the unit ball $\mathbb{B}_X$ of a complex Banach space $X$ into the closure of the unit polydisc $\mathbb{D}^m$ within the space $\mathbb{C}^m$. First, we…

Complex Variables · Mathematics 2025-11-25 Vasudevarao Allu , Raju Biswas , Rajib Mandal